I think there is some confusion here.
Derailleurs are gear systems for Chain and are INSTEAD of a gear box like the Kindernay.
If you have a Kindernay Gear box, you do NOT have a derailleur. What you do have is a Tensioner to take the slack of the chain when the rear travel changes with the suspension. In order to take all the slack created by a Full suspension MTB, this is usually a dual wheel tensioner.
If you want a belt, you also need a tensioner, but in addition to being able to take the slack, it also needs to provide enough tension for the belt (way more than for a chain). So far, belt tensioners that can provide enough tension are single wheel and usually cannot take all the slack of the belt on a full suspension MTB.
A dual wheel tensioner with enough tensioning strength for a belt could eventually be developed (I happen to know because I designed and built one
) but has not been done and released as a functional solution by any manufacturer.
So Hydras, for now, cannot have a belt drive