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Only if you use an infinitely long sinc filter. In practice, there is always some error. The error can be made arbitrarily small, but never zero.
No, 64 bit double precision math can round to bit perfect results at 24 bits and certainly 16 bits. Remember bit perfect only matters to the supplied resolution, rounded to 16 bits if you start with 44.1/16 is all that matters.
I am assuming you keep the 48k data in double precision floats, so yes an unrealistic example.