I don't see why not. Even real life militaries have squadrons composed of different aircraft. Moreso if the unit has actually been in combat and suffered losses.
Mismatched squadrons will happen despite best efforts, and yes moreso in merc units - you'll see that effect yourself if you play in that kind of game campaign. House militaries in the post-Helm era should be able to ensure at least flights are homogenous... but then again as upgrades roll in, they might not be of the same variant. Again, this also happens IRL.
Building on this, the Helm Core would make supply
easier due to providing the info needed to fix up the factories to improve production rates. As for the old variants they'd gladly get rid of, there's always mercenaries who'd be glad to take that junk off their hands...
As for how frames spread, I favor the trickle-down theory. High-priority unit is told that they're getting a shipment in of new, upgraded fighters to replace their current birds. The pilots transfer over, and the suddenly vacant lower-tech birds are sent to lower-priority units that have holes in their formations. Any excess is then sold to mercenaries on-contract who have need of fighters.
I favor the same theory in regards to how most mercenary units acquire BattleMechs. High-priority House units get new, shiny equipment that has the latest tech as factory standard, the old stuff they don't need anymore is sent down the chain, the lower-priority units take that excess equipment to upgrade themselves and send
their old stuff onward, terminating with mercenaries and local militia.
Incidentally, this is why, if I'm making a post-Blackout mercenary unit that has a stable contract with a Great House, they get mostly Jihad-Early Republic stuff the House units have been getting rid of as they upgrade. And considering the eras in question, there'd be a
lot of surplus equipment. But that would mostly be to give players something
resembling a fair fight without having to take Clan Invasion-era (or worse, Succession Wars!) equipment up against Dark Age units loaded up with shiny tech.