Yes. Goblins are active in every season, and every season enemies randomly decide if and where they want to send sieges. If multiple enemies decide to besiege you I think the one that reach you first is the one you'll usually see, while the others normally reach your site, see that it's already under siege, and go back home.
I had a curious case where a necro tower appeared to do a hello/goodbye siege where a single unit showed up and disappeared immediately after the game was unpaused. Shortly thereafter the neighborhood gobbos showed up for a siege, and shortly after that, one of my dorfs running for cover discovered two stealthed necros from the first siege (unfortunately they weren't massacred by the gobbos, but left the map unmolested).
I've seen 5 attempts to besiege my fortress at the same time at an embark with 7 necro towers and one gobbo civ, using DFHackery to find the army commanders.
Thus, you're lucky if you're not besieged in any one season, and it's a decent year if you've got one siege free season.
One thing you can do to catch up is to just turtle and do the cleanup (and possibly a bit of rest on top of that). Apart from that, you'd need to decimate their numbers to the point at which they aren't able to attack you any more. That's probably not possible with 10000 strong dark fortresses, but if a civ consists of only smaller holdings it might be possible. Conquering the weakest civ's sites might work to gradually reduce your number of effective enemy civs to 4.
If you're going to make a mess out of the enemy forces, I'd suggest some kind of industrial scale semi automated atom smashing or magma burning of the invaders and their equipment. Magma will burn most of the stuff, meaning that only the good stuff (iron) remains, but also requires the traps to be fully magma safe.
Also note that with the volume of invaders you're likely to process, loss of some of the goblinite to atom smashing doesn't really matter, as you're going to get more metal than your fortress is likely to be able to process (let alone used), via the goblinite home delivery service.