I successfully used peat pellets on non-peppers in the past. However, I am not using them for my peppers at this point, but did put a few just-sprouteds into a couple of them about a month ago. At the same time, I put some just-sprouteds into some starter mix. The ones in peat pellets did come up, but the ones in starter mix did not - finally dug them up and found they never went any further than when I had put them in there.
You said you placed your sprouted seeds into the pellets, so I am guessing you are using the paper towel (or similar medium) method for initial germination, then moving the just-sprouteds into the pellets. I am doing similar, but now am not moving them into starter mix until they are more fully sprouted - the sprouts must be green and tall enough that I can safely move them to the starter mix with the tops above the surface before I move them. They're still very small at this point, but at least I have evidence at the surface of what is going on with the sprout.