Can a hot tub be installed in a utility room?
Expensive homes have indoor pools all the time, however they also have rather sophisticated air ventilation systems.  Without it you would have uncontrolled mold accumulation. No matter how tight the lid is on the hot tub you are still going to introduce a lot of moisture into the house that other wise would not be there. I would recommend full exterior grade paint on in this newly and entirely finished utility room. Weatherproof exterior grade doors should be included in the room with no open air space shared by the main part of the house and this utility room. All adjoining spaces will need to be weatherproofed and caulked. No shared HVAC system components or duct work.  And last but not least you will want a fully controllable and robust air ventilation system that is sensitive to temperature and humidity levels.