Sodium Thiosulfate is the active ingredient in standard fixer, and it's the same thing as what's in the de-chlorinator. But you don't know what else is in there, and whatever else (if anything) may or may not be detrimental to the photographic process.
There are other reasons why this stuff may not be a good idea. Formulating a fixer is not as simple as it seems at first. If you're using an acid stop bath (and you should be despite what the naysayers proclaim), the acid carried over into the fixing bath will destroy the thiosufate in short order if there is no sodium sulfite to act as a preservative. Whether you decide this to be an acidic, neutral, or alkaline fixer, you'll need a buffering agent to maintain the required pH level. Bottom line is that if you're doing this to save money, you're not really. A very good and inexpensive fixer is Kodak's Flexicolor fixer and replenisher. It's made for C-41, but it works just as well for B&W materials. A gallon of concentrate can be had for about $10, and when used for B&W work it can be diluted to 1/2 strength to yield 10 gallons of working solution.
Chris, there's no need for a fixer to be acidic. There are plenty of alkaline and neutral pH fixers on the market and they work just as well as the acidic ones. The Kodak's Flexicolor fixer comes in at around 6 to 6.5 pH, and that's only slightly acidic.