Can Sparse Fourier transform be used for sparse signal in other domain
No.

What did you expect? For sparse algorithm to work, the signal has to be sparse. If it's sparse after a integral transform, that doesn't mean it's sparse under a different transform.

Also note that according to this answer, the benefit of the sparse fft only apply to very sparse signals - a factor of at least about 2000 between the zero and non-zero bins.