Now my other question is will not using stop bath kill your fixer faster?
No, if you wash long enough. Acid stop bath indeed helps to maintain fixer pH, but this is relevant only if you compare to single water bath (or no bath at all). If you do 3 to 4 subsequent washes (water changes), as suggested everywhere, it will dilute the alkalinity to practically zero. There is some dilution of fixer (thiosulphate), but this is true also for stop bath.

And if you are so worried about water bath not being good enough for process or fixer, don't even think reusing the stop bath. Developer keeps accumulating to it . The only thing it does is maintain pH.