Can the rings feed cables into vertical cable management at the side of the rack?

Yes. In fact, that is one of the more natural ways for horizontal and vertical management to work together.

The rings organise the journey across the rack, then the cables leave at either side and join the vertical route.

They are handling different parts of the same journey rather than competing systems.

Trying to make a horizontal manager perform the entire vertical run as well usually produces a rather meandering result.