Technically electrolysis separates water into basically air so it's not simply parts of the water cycle going from seawater, to clouds, to rain, to fresh, to aquifer, etc. And I imagine in the wonderful world of industrial chemistry and materials manufacturing that H20 is used in a number of chemical reactions whose result is not returning an identical amount of H20.
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.