I think the usefulness of dumbbells for assistance exercises depends on the individual gymnast.
A weak gymnast who can't even do the basic progressions could use dumbbells for assistance exercises, but he'd probably be better served by doing dynamic strength work.
Dumbbells obviously can be used to scale as well, if spotters or other scaling devices are unavailable.
In my uneducated opinion, dumbbells are most useful for intermediate-advanced gymnasts who can already do the static holds, but need the extra work either to develop the muscles or to sustain the muscles in the necessary joint angles and in the transitions between holds. I reckon getting on the rings and training can be extremely stressful on the body, so it may be wise to utilize dumbbells during certain periods of some gymnasts' training cycle.
Of course, more advanced gymnasts already have core strength and body control, while beginner-intermediate gymnasts may not. That needs to be kept in mind in deciding whether to implements dumbbells or implement scaling.
If I'm off-base, Steven or Blair can correct me.