Yes, my very first playthrough of the EA, I avoided using the illithid powers since they are evil and I was playing a good character, and I had no dreams at all.
I haven't tried a Paladin yet, but does using the illithid powers break the paladin oath?
Not the oath of devotion. Or at least not for my paladin, which is about as much as I can say given how wonky the oath breaking mechanic currently is.