There's no conclusive evidence either way. Despite strong suspicion Ascians were involved with the Ul'dahn Revolution arc after 2.55, nothing has come of that. Lolorito turned out to just be using the Handmaiden as a pawn, slipping Nanamo a different poison (one that asphyxiated then made her comatose... however that works).
It's just in peoples' nature to suspect the Ascians will be involved with Omega, given Lahabrea was so closely involved with the Ultima Weapon and the two are functionally similar. Ilberd is also a rogue element who would benefit greatly from having that kind of power at his command, so naturally people are going to try and connect the two.
That said, Omega is still a scrap heap buried in Cartenau. Given this, the fact it would take numerous master machinists to refurbish it quickly, it still needs a fuel source, and that the Ascians are going to take a more backseat approach for 4.0, the chances of them helping Ilberd (etc.) excavate, refurbish, and fuel it before then seem slim at best.