If you load your .222 to "standard" pressures, 45 kcup, they'd likely work. The 6 1/2's were Remington's standard SR primer before people started shooting .222's in BR competition back in the 50's at pressures that nobody at the factory had intended. The 6 1/2's couldn't take the pressure and 7 1/2's became their standard small rifle high pressure primer.
If you never exceed the loads listed in most manuals and use EXACTLY the same components you might well be okay. Otherwise I'd only use the 6 1/2's in a Hornet, Bee, .25-20, 32-20 or similar low pressure rounds.