You 'can' sit too deep on a horse...absolutely, without a doubt. Does that have to do with the depth of the saddle seat...no.
I prefer a deep, soft seat myself. It's a personal preference and it also based on a number of other factors...unimportant for this conversation.
I agree that if you are 'locked' into the saddle such that you can't properly cue the horse, or you find you are constantly having to adjust your pelvis, thigh, pick a piece of anatomy, to remain in the correct position, then the saddle doesn't fit you and you need to keep looking.
So, try the saddle out...see how it feels and also make sure to have your instructor, or a good pair of eyes on the ground to make sure you aren't changing one bad habit for another positionally.