If they have the same hairdryers on Summit that they have on Infinity, definitely leave yours at home. They have them in the bathroom and they are so far, the best and most powerful ones I've seen onboard anywhere. I would think they are the same, hopefully some Summit cruisers can say for sure.
Have sailed on Summit and yes, there are hairdryers in the bathroom. They do a super job of drying the steam off the mirror in the bathroom after a shower. However, if you have thick hair that needs lots of styling, bring your own blower.
Love the Summit and the bathrooms, but did not like their hair dryers! They get so hot they are painful to hold. Have read lots of other posters who are in agreement- bring your own dryer and dry your hair at the vanity.