Alternate universe sure this could work but I would have trouble buying into this one for a current-FSverse explanation for the shivans.
For several reasons, along with those already being debated, secondarily;
We did nothing to trigger the first Shivan invasion.
Neither specie had anything like the kind of tech to influence subspace in that fashion, not GTI nor PVN Intel were even close.
It's also hinted that the GTI knew quite explicitly (in the original ST, not just ST:R) that the Shivans were around and incoming.
It is an original(well, ish) and decent idea (I do like it) for sci-fi in general but it wont work in the direct FS Universe established as Canon in my eyes, even as Fanon, it's a bit too much of a stretch, at least without some serious fleshing out.
But yea, in an alternate universe you could make both specie more advanced in terms of subspace management and then explain away the reason between the difference in FS1 and FS2 Shivan behaviour (since your campaign explains their origins it's going to have a better understanding of them).
But the likelihood of a immediate formation of a complex organism with such diversity but a singular language and single type of 'cell' inside (which is just about the only way you'll be able to explain it away (the ships being alive/The Shivans) without going from sci-fi to biblical fiction as mentioned before, though the thread serves as a useful reminder to how easy it is to make religious **** up) is lolworthy.
As for the infinite improbability drive, being a comedy, it was created by a finite improbability drive by a student because he realised that if they had decided that if the infinite improbability drive was a virtual impossibility it had to be a finite improbability it's a pisstake that Adam's wrote about on **** like this ;p