It's not very wise to make guesses. This is not something one can guess.
I'll do it anyway, though.
Our real nature is not dependent on mind, that I think I can say with certainty.
Recognizing it is a different matter though. For instance, one may receive transmission and not being able to recognize rigpa, at least one won't discern it. Then one practices to gain such recognition. In the transmission process, I'm not sure if we can say mind's involved. Maybe Namdrol can clarify this better. In the practice per se, like preliminaries and that, I'm pretty sure we can definitively say we are using our mind. Nevertheless the word dependent
points to a relation of cause/ effect and that may be a little problematic in a Dzogchen context, but obviously mind is involved in the overall process. For instance, imagine I receive transmission and I think (mind) "I haven't recognized rigpa" or afterwards "I have recognized rigpa". According to the experience, we practice, some to gain such recognition, others to prolong it. I'm sure mind's involved at several levels in the whole of the several practices we may end up doing, but it is not mind that causes the recognition of rigpa.
Maybe Namdrol could clarify this.