Nope, ants generally do not pose a risk to pepper plants unless they are "farming" aphids. Aphids secreet a sweet substance that ants will consume. But then it is an aphid problem and not an ant problem. The ants themselves pose little risk to peppers. Likewise, they do little good. They are very poor pollinators unfortunately.
Bruce

If the ants bother you by being around your plants, cinnamon they hate, sprinkle on the soil or at the base of the pot and they avoid. As Bruce said check for aphids as ants can be a tell tale sign of aphids and they will protect aphids and ward off predator bugs for the return favor of a sweet treat.

Mark

OK, guys. Thanks for the insight.