There's one way to find out. Pull the rubber band and see if the peep pulls back the same after every shot. Shoot at like 10 yards while you are testing. The post the tubing attaches to might throw it off each shot though. I've seen people using them without the rubber band attatched though.

One way or another you'll have your answer well before deer season. If it doesn't work out just put the rubber band[:'(]back on.
I've been able to true a pee with crappy stock strings before. I'd think it has already moved whatever it will before it starts to break down (not anytime soon).

BTW, have you added the TR DZ upgrade "O"-rings to your rest yet? or does it already have them?
If you are unsure, raise the bar and look below where the arrow rest bar lands along the shaft it rides upon. you should see 2 o-rings beneath where the bar lands. (clear as mud hugh?)

If you don't have them contact TR and request the "upgrade kit" you'll get 4 tiny o-riongs and some instructions in the mail asap. 4 free.