Hello Tesseract,
I think growing peppers and cucumbers in the same system would work well. Their both continuously fruiting plants with similar
nutrient needs, as well as lighting needs. Their both large plants and would do well in a
drip system. Determinate pepper plants are bush variety, while cucumbers are vines, so they will both need different types of top support. But that's quite simple and easy to do.
But with that said there are some environmental concerns that wont be an issue growing outside in natural sunlight, but can be a problem growing inside. Most peppers are self pollinating so they just need air currents to pollinate, but cucumbers need to transfer polling from male male flowers to female flowers. So if your going to grow them inside, you need to hand pollinate them yourself. If your growing them inside, because their both large plants as well as fruiting plants, the lighting will not only need to have good light intensity, but good even coverage as well.