As far as git is concerned, GPG is a black box and git feeds it normal git hashes, of which there is only one kind. This design makes sense.

For anything else, it depends on the exact scheme:

If git sent GPG the bits for the current commit specifically because it expects a better hash to be used, that would be silly to design on purpose (git should use a hash that meets all requirements). And it wouldn't protect history, which matters.

If git rounded up the bits of history, that would perform unacceptably badly.

If git used a better hash to secure history for signing purposes, and still had the normal hash elsewhere, that would be very silly to design on purpose because it should use the better hash for everything.