I don't think we would be able to clone any life we find on mars, because we don't know how their dna/reproduction works, and even if we did, we wouldn't know what nutrients the embryo would need, and in what amounts.
One of the exciting things about finding life (actual, or remains of) on Mars(/Europa/wherever) will be to see if we can
find out what a non-terran form of life is like. Currently we know there's
our way of 'doing life', but that there's almost certainly other ways. I'd be very surprised if an independently arising life-form had the same (deoxy)ribonucleic acid base to it (although a double-helix mechanism sounds logical for both data reproduction and packing purposes, whatever the substrate involved actually is) never mind having exactly the same AGCT(/U) bases, and the chances against any
same sequence mapping to the
same purpose (certain triplets mapping to certain identical proteins, other sequences mapping to particular 'parsing instructions' by the replicating/maintaining enzyme-equivalents) would be astronomical. There'd probably be no Martian-Human hybrids possible (even assuming we both turned out humanoid and
physically compatible, insofar as reproduction were concerned) due to the total mismatch of the respective gamete chemistries involved.
Unless... What might be even
more interesting (while leaving the above question still open for vastly more remote cradles of life), is to find that we
do share something with this other life we find. Because for all except the most minor similarities and 'universal principles' behind the way that life works[1], this would give a high probability of indicating a common ancestor at some level. Whether life from Mars seeded Earth, life from Earth seeded Mars, or both were seeded by the same external agency (everything from dumb interstellar panspermic cometary fragments to actual "intervention by a 'Progenitor' race"), we may miss out on discovering something
totally new, but we'd get some quite exciting possibilities laid in our laps, for us to argue over until we can find yet
another place (or three) where similar life has arisen (or the source), and let us start to narrow down the relative histories.
Really, it's win-win. As also is "there is (and was)
no life on Mars!", for a different reason, except that it would be much harder to prove such a negative. And we'd necessarily have to send even more probes to make deeper tests for life, rather than more complex probes (or sample-return missions) to
analyse the life we find... But it'd be nice to get all this done before we consider a Red/Green/Blue Mars terraforming of Mars (and areoforming of humanity), which would almost certainly obscure and overwrite all the evidence we might otherwise have found. (Or, at the other extreme, tap into something that wipes
us out!)
(BTW, by mentioning "embryo", I believe you're thinking of much 'higher' forms of life than I'd be comfortable even considering... Looking at cloning (without the luxury of being able to do it 'in vivo' with a related/same-species foster mother), we'd be fairly optimistic to consider anything beyond bacterial/slime-mold level, and even then we'd need to have full disclosure of the nature of the genome
and proteome (or whatever equivalent(s) exist for this 'alien' organism) plus a decent equivalent cell-wall set up[2] to enclose the mix that needs to be rigged up (or, if we're lucky and it's pretty much the same as an Earth organism, taken from a flushed-out donor). The majority of the cell wall can probably be anything 'neutral' (a lipid-lipid system such as our own), but may need augmenting with certain features (such as specific ion-channels, dotted around it) just to have the single cell 'live'. To get the cell reproducing, though, we may need to ensure that the 'given' cell wall is completely compatible with whatever
additional cell wall components get produced and shoved into the structure both before and after cell-division. But I'm also rather simplifying the degree of complexity of attaining even the former state. For one thing, nothing we've sent to Mars has the ability to do anything like the chemical analysis needed to transfer even the most basic parts of a
known cell's biomolecular makeup as data for reconstruction in an Earthbound lab. Sample-return is the way to go, really, if we can get a biology-friendly containment vessel between our two planets without undue delay, or are happy to work on 'remains' of life for starters. Still gives us the "nutrients" problem, but hopefully we can get enough "environment" matter to work out what is being fed upon.)
Anyway, that's way beyond Moon Bases. Although on that topic I still contest that while inter-planetary travel would probably rarely deliberately stage via the Moon (landing there and taking off would be wasteful of the 'orbital potential' already gained), Moon-manufactured components and other resources (at least until we
do get sufficient asteroid-mining operations set up) are going to be better value that Earth-sourced ones, plus we'll have an infrastructure to receive certain 'lifeboat' missions and a more convenient place for permanent off-Earth residents to reside where gravity only needs augmenting (not creating from scratch) and where bunkers against solar flares are 'merely' a matter of excavation into the regolith and such, rather than accumulating sufficient shielding.
i.e., we may no longer need to use the stepping stones across a river once we've set up a decent bridge that even non-pedestrian traffic can use, but stepping stones may be useful while
getting that full-on bridge built. At least in the early stages. (Stretching the analogy even further would be foolish, so I'll stop there. YGTI.)
(Finally, I'm not sure I'd go with full-on VN-Machines, but basic manufacturing machines (semi-unmanned, if not totally for the simpler devices providing the simpler end products) would probably be the seed needed for a more complex moon production facility, anyway. Ignore the self-replication aspect[3], but there's going to be some savings in lift-weight if we send the right kind of stuff near the beginning of the endeavour.)
[1] What we currently consider a "universal" in life may not be. See footnote 2 for a possible big discrepancy (and the next two sub-footnotes for a 'substrate-shift'). And this is without considering replicating systems of life that aren't restricted to carbon-based chemistry[1a] or even
any chemistry[1b].
[1a] Although silicaceous equivalents almost certainly have a differing "golidlocks zone" that neither Earth nor Mars have ever resided in.
[1b] Magnetic field/plasma-twist 'beings', as one not particularly far out example (although these would be even less likely to liuke the Terran/Arean environments, or at least their surface conditions (in the magnetosphere/aurara?), and perhaps be inhabitants of stellar chromospheres, instead, or elsewhere. Whichever way, well outside the remit of a Curiosity Rover survey.
[2] There may be solutions to the equations of life that do not need cell walls. However, these would probably be so different an organism (see footnote 1b for a little speculative musing) that I'm wrong even about the genome/proteome equivalence components, as well, so I hope you'll forgive me for skimming over this little awkwardness of terracentric thinking.
[3] Aside from everything else, everyone's seen enough SF to know that there are certain things we don't want to encourage our machines to do so easily.