I don't think there's a universal answer there, it would depend on how accurately they can fingerprint you without GTM. Blocking it does remove an identifier that would make it easier, but blocking it is also a piece of data that could feed into the fingerprinting algorithm.

It would be interesting to purposely feed a bogus GTM cookie though. It might actually throw their tracking and fingerprinting off if somehow you were able to send random GTM tags on every request.