PAPR (Peak to average power ratio) of OFDM signals
Will the PAPR of an OFDM signal using QPSK modulation on its subcarriers be different than the PAPR of an OFDM signal using QAM256 on its subcarriers?


No, not in general, which an easy sum notification using the QAM and PSK symbols in amplitude&amp;phase notation would have yielded.

Of course, you still have the central limit theorem, but that's exactly that: a theorem about what happens in the limit, and you haven't defined the number of subcarriers.