Your central question first:
My question, does the results of FFT in frequency domain must be sparse since its equivalent time signal is sparse too ?
No. In fact, it does the opposite: signals sparse in one domain are typically dense in the other.
If you want so, that's happening for the same reason that we have Heisenberg's Uncertainty Principle: Operators like the DFT don't allow us to preserve correlation / concentration of energy when going from one domain to the other (or back).
Let me comment on your original statement:
In OFDM system, if we have a multi-path environment, we supposed to have a sparse received signal in time domain, then FFT is performed to convert it into frequency domain.
That is false. The characterizing property of multipath environments is that they convolve the transmit signal with a nontrivial impulse response.
That converts even very sparse time-domain signals (e.g. a single dirac impulse) to dense ones. The only case where a channel would introduce sparsity would be if the the impulse response of the channel happened to be a matched filter to the transmit waveform.
But that can not be the case for an OFDM system, as that would directly contradict the principle of OFDM which is that you transport different bits of information on different frequency bins.
You might be considering a predistorting system, but then you'd mention that, and also, you'd know about the spectral properties of your signal (and hence could've negatively answered your original question yourself).
So, it feels like you've either taking something completely out of context, or you're misunderstanding something fundamentally.