No, x87/MMX and SSE XMM were not aliased. They were two separate register files.
(You may be confusing it with XMM vs YMM vs ZMM, i.e. SSE vs AVX vs AVX512.)
(You may be confusing it with XMM vs YMM vs ZMM, i.e. SSE vs AVX vs AVX512.)
But the OP was talking about Intel's P3... so 3DNow! wasn't a factor...
SSE never had aliasing, so OP’s comment is strictly incorrect either way.