Since this likely custom house has two garages one for cars/workshop and left one for a bigger thing, RV maybe?
I'm 99% sure that OP means the left garage area 15x33. I think it could work fine, but you'd need to delete that tall garage door, put wall and insulation instead. you'd probably need to add insulation to side walls as well.
Other than these "minor" details, I think you could definitely build a proper HT room. due to big height, you could even go for 2-3ft elevated 2nd-row seating.
Before purchasing the house, I'd bring a constructor or five to give you their estimate. You guys have lots of building codes and converting garage to HT room may bump into some of them.