Can XPS foam support the weight of a bath?
It depends on what you mean by "support". It will hold the tub up but it will flex. The movement of the flexing may loosen plumbing connections ; not the first time , but movement over an extended time could work things loose. It may even cause leaks at what ever caulk or trim is used on the top edge of the tub.The weigt of 6" water in a 5' tub is roughly 300 lb. plus occupant(s).