It might; I don't know.

In general, the TSP / STPP substitutes are FAR less effective than the phosphate products. If you concerned about phosphates in the wastewater . . . fertilize your garden with it, when you're done. But if you get a good garbage can, and spray off your cartridge before soaking, and add 1/8 cup of bleach with each cartridge . . . I don't know a reason why you couldn't use the same solution all summer. You'll probably need to add another cup of TSP mid-season, though.