Will a bad camshaft position sensor cause sputtering while driving?

My 05 Sierra has what I presume to be a bad cam sensor. It backfires on startup and when I de-accelerate. Now it sputters and looses power when I first go from a stop or when I'm doing 65 and accelerate to 80. Oddly enough it only happens when I press the pedal lightly. When I mash the pedal down it doesn't sputter. It doesn't have any cel codes for the cam sensor. The only codes it has are large evap leak (this was on wayy before the backfiring problem) and cat codes (also before the backfiring). The only vehicles I've owned in the past are Saturn S Series cars which don't have cam sensors so this is a new one for me.