You should be ok in May, be aware that the Taylor is a snowmachine trail in the winter (not plowed). If there is a big late dump of snow, you might have an interesting couple of days. Some cool country up there though, and worth the trip even if you did it later in the summer as a side trip.
Driving to Deadhorse is certainly doable. Just keep in mind that it is a trucker's highway, and it belongs entirely to them (just ask). It is a gravel road, and sometimes 70mph is too slow and you'll be holding trucks up. But I'm sure they will figure out a way to let you know if that happens. I'd bring a couple of spare tires, and you'll want to figure out your fuel situation before making the trip. A CB isn't a terrible thing to have there either.
