If you are okay with regular seating, sure that is an option. We usually tend to get Green Car (First Class) which the JR East Hokkaido pass doesn't offer (only the full country wide JR pass does, but that one is too expensive these days and harder to break even).

I'd still add up your different main train trips planned and see if it is cheaper with the pass or at least close to break even. If yes it is more convenient with the pass. If not even close it may be better to book individual tickets.

If you want a special treat, Grand Class on the Hayabusa is very nice. We did it once for the experience, but of course it is more expensive and you would have to pay extra on top of your pass cost. Just mentioning it. Regular cabin on Hayabusa is perfectly fine and comfortable.