Same general thing, different details. Whether "the search process" is within an A* search or between them.
If the job "goes idle" until the next slot then it won't complain about no route but it will go unfulfilled in one simulation where it might in another, with no in-game reason.
It might be serviced the next time there's an attempt to run through job-associations. Does it get priority next 'tick' as remnants of the old tick queue, ahead of anything new/renewed, or is it still at the same possible unreachable end of the rebuilt queue? Depends on how it's coded[1] by the coder or his chosen library functions, but there's possible differing handling that could confound all existing expectations on rare occasions.
Just mentioned for the potential curiosity. Increasingly not part of the root of this discussion, I know, just a (risingly convoluted) trivial aside.
[1] Assuming that the effort to check each job averages significantly more than the "choosing" code needed to implement this, I'd probably consider something like pre-weighting/grouping candidates with priority values and checking 'N priority-N' jobs for N=N.max downto 0 (within a wider loop that continues until all jobs or time available to assess jobs become depleted), and within each "N jobs" bit randomly pick the (up to) N jobs to try in this particular pass. Could just be random-plucking without the weight-groupings (which could also be dealt with by something like "N² priority-Ns" if you wish) but I'm imagining there's good reason to (e.g.) set "Trying to Moodcraft" as more urgent than some other jobs I could mention (for the game, whatever the player's thoughts are about the relative needs of Dumping, Smoothing, Deconstructing, etc, though "Do This Now!" tasks could be given something like an N+=10 adjustment on behalf of the clearly frustrated player) the basic idea is that the overall chances of non-choosing go down each time it slips through each instance of choosing made, just by statistics, without ever having an 'untouchable' class of jobs either. It just smooths out the 'bad luck'. It's also very unlikely to consistently hit/not-hit the problem I was describing as the Heisenbug on the same machine, which might still be awkward, but not in the way I originally described.