Headroom will be a thing; peppers will grow taller than that arm can probably accommodate. Some varieties tend to grow low and laterally, and/or you could trim them (though that might affect their productivity).
If you want to grow a pepper plant to maturity I'd stick with just a few, culling all but one. More light might be in order, too. I've grown perfectly healthy chile plants in half-gallon jars, but it takes frequent top ups.
Poke around here, use the search feature for guidance. We have quite a number of excellent hydro gardeners and many old and new grow logs packed with general information as well as tips and tricks.