Water is just moved from a useful (to humans) state to a less useful state. The bottom of which is seawater. Seawater is still useful, it just takes more energy to do it. There's an unlimited supply of less useful water.
All that to say that once we use the easy water, that cotton shirt is just going to cost a lot more.
However I do believe that the vast majority of water is probably returned to the water cycle in some form.
I think the big thing here to discuss should be power cost, not water use. How much power did it take to make that t-shirt, including the entire power cost of the water and other materials required. As you say, that power cost will increase dramatically when we're desalinating instead of pumping.
Yes there is an unlimited supply of seawater, and there are also a lot of places far away from seashore in regions with scarce water where people live, and once that scarce water is used it's not a very livable place anymore.
See also the history of the Aral Sea, nearly completely disappeared because of Soviet cotton industry.
Someone there made the very sobering observation that the solution to the problem was to price water the way we price oil. That way we would redouble our efforts not to waste it.
But then that only really ends up punishing the people least responsible for the crisis in the first place.