Intermediate is pretty much what it means. Can you comfortably ride an intermediate slope at a resort?
I am guessing by your trepidation and initial post, if you book a cat trip, you should do it at the intermediate level. Nothing wrong with it. I spend plenty of days in the backcountry in terrain that would be considered intermediate. In fact a couple of my favorite runs at Bert are intermediate in nature, but they are just fun. Sounds like your goal is to ride powder, not necessarily the steepest, most gnar pow runs you can find. Take it easy, book it for an intermediate level day. You'll be riding powder all day and that never sucks.