The rules really depend on who's writing and what kind of world they're building. A lot of the foundational stuff, especially the early fanworks and mainstream ABO, stuck to a pretty strict biological binary: Alphas impregnate, Omegas get pregnant. That's the whole dynamic, right? The tension comes from that power imbalance and the biological imperative. Saying an Alpha can get pregnant sort of flips the script on its head.
I've seen it happen though, mostly in stories that are deliberately playing with or subverting the trope. It's often used for shock value or to explore themes of vulnerability in a character who's otherwise dominant. Sometimes it's a rare biological anomaly in the universe's logic. I read one once where an Alpha on specific suppressants could temporarily enter a receptive state, and it was framed as this huge taboo. Honestly, it made the romance feel more forced than revolutionary, like the author wanted the 'shock' without fully committing to the worldbuilding implications. It broke my immersion because the rest of the society reacted with this over-the-top horror that didn't match the otherwise modern setting.
If you're looking for it, you'll probably find it in newer, indie-published stuff or in specific sub-niches that focus on mpreg across designations. But in the bulk of what I'd call classic Omegaverse romance, it's treated as a biological impossibility. The genre's conventions are built on that specific fertility role, so changing it changes everything about the power dynamics the plot often relies on.