I think it's unlikely for a few reasons. The biggest reason being that F1 is sold out at most permanent race tracks (non street circuits) these days.
Having raced both cars and bikes at an amateur level, I don't think the safety features are similar enough. You move a lot of air fence/tecpro and widen or lessen gravel traps to switch between cars and bikes.
They may once for a promo type of thing, but I doubt it'd be a consistent thing. Happy to be proven wrong for sure, but it seems logistically too tough.
That would be really cool. I'm not very familiar with MotoGP, but they have different curb/runoff/etc. requirements, right? Are there a lot of F1 races that meet requirement for both series? I know they already share some tracks on different weekends.
My understanding is that most if not all dedicated tracks that F1 races on could be Moto GP tracks, but street circuits would be no. The bigger issue is the loss of good GP tracks that F1 could not use. Like Laguna Seca, it has one of the best corner complexes in racing but F1 can't race there. And we all know they would axe moto GP races before F1