Yes, it's possible. You can use transient noise for anything. However, it won't be anywhere as efficient as pnoise. The benefit of transient noise would be that you can see large signal noise effects (which are not normally a problem for mixers), but the downside is that you'd need a long simulation with short timesteps to capture all the noise information. pnoise just requires you to do a PSS on a single cycle of the mixer LO, and then an efficient small-signal noise simulation after that - akin to how you would use noise around the DC operating point of an amplifier rather than using transient noise for that.
Transient noise is a bit of a sledgehammer to crack a nut in this case.