I decided to do something silly, just to see how long it would work. Turns out the answer is longer than I expected, but not as long as I hoped.
I fired up a 40-planet Fallen Spire game, 7/7 random easier/moderate, no exotic options on, and found a snake map with a starting planet all the way at one end with autobombs. The goal was to see how far in the FS campaign I could get using only an autobomb doom cannon (multiple space docks with engineers pumping out autobombs set to rally on FRD in whatever system I was attacking), with bombers as the only other unit I was allowed to use, solely for cleaning up the things the autobombs couldn't, i.e. missile frigates (which are immune to area damage, and thus autobombs) and force fields (which are inexplicably immune to them and just make them vanish, not even explode doing zero damage). If I were so lucky as to make it far enough as to get Spire ships, then I could use those, too. Oh, I also didn't capture any planets other than my starting one, because I'm mean to myself. Heh.
Not to give away the ending right up front, but...I didn't win. It was pretty hilarious at times, though. The first couple planets were pretty trivial to plow through. It started getting a little annoying when the autobombs made it to a system with a force field, which they were very determined to throw themselves against completely futilely, even though there were plenty of other valid targets. It's weird, because nothing in the force field's list of immunities suggests that it should be immune. If they're supposed to be for balance reasons, it'd be nice if it said why and if they were smart enough to not just bash their heads against them...
Anyway, I got my micro on and manually bashed their heads against the correct things, used the bombers to support them when they needed it, and got the first shard pretty trivially. You do not make the autobombs angry when there's a constant stream of them heading your way that's bigger than your constant stream of wimpy ships.
It started getting a little more annoying, as pretty much every system after that had a fortress (imagine my retroactive lack of surprise to learn that it was a Fortress Baron) and at least one or two force fields or shield sphere guard posts, but the autobombs marched on. It takes them a long time to kill fortresses...
Incoming waves were pretty amusing to watch fail, even with no defenses, especially the usually-harder-than-normal bomber waves which died twice as quickly. For some reason it started fixating on missile frigates, though, and about 50% of the waves were those, which the bombers had to deal with themselves, which slowed things down. A mk4 planet also got a bit tedious. Never really much of a threat, though.
The next shard/ship/whatever was only slightly harder, and that got its outpost and ships built pretty quickly with all the resources I had nothing better to do with. I exploded a path to the third one, hoping to actually get my first city going, and was sort of surprised I wasn't dead yet. I still hadn't run into anything scary, which seemed a bit odd.
The survey ship finished doing its job, I sent the shard on its way, and the bombers and four measly Spire ships tagged along behind it. It started out pretty well, but this time the autobombs couldn't really keep up with everything, and eventually that meant the bombers and everything died without the suicide squad doing its job properly. The real problems were the Core Starships and other crap like that, which can just march across an entire system or three ignoring the dozens of ships ramming it, unlike most smaller starships and guardians. I actually had the shard in the system next to my homeworld when it died, but it didn't quite make it.
I suspect it's probably possible to make it a good deal further if you're a bit luckier than I was, play a bit smarter, micro a bit more, or use a slightly less masochistic variation on the rules I used. Heh.