That probably varies. I'm not actually even slightly familiar with the design of these chips. At one extreme, I know you can have a software defined radio (possibly with limited range) and do everything in software. But in practice there will be dedicated hardware for at some things, like acquisition hardware that tries to lock onto a specific satellites prng encoding.

I'm not sure if the position calculations themselves usually use specialized hardware, but I would expect that processing of most data frames is handled by a small embedded processor, simply for flexibility. If the position calculations are done in software, then updating to use this data is probably possible in some designs with just a firmware update. Even if the position calculations are done in hardware, I'd bet the parameters are passed in from the software on the embedded processor, so it sounds like the conversion to the traditional parameter could allow that to be reused, as long as the design does not try to reuse these parameters in other ways which could cause trouble. If it does then the new limited Ephemeris data cannot be used, but the parity data might still be usable to improve time to first fix.

But all of this relies on the SOC supporting upgradable firmware for the embedded processor, that the SOC maker actually develop and provide that new firmware, and that the device manufacturer decides to incorporate that firmware update into a device update.