Not just for melody, but also for percussion this can be used. I recently attended a workshop Japanese Taiko drumming from a world touring Taiko drumming group.
They teach the rhythmic patterns by first singing them first. They use vocal sounds as tiny phrases which translate to the hand/arm movement (in Taiko drumming, not only the drumsound is important, also hand and arm movement are, it's like musical karate). After just over 2 hours of practice, the workshop group was able to perform a 2,5 minute piece !
I didn't use singing/humming that clearly yet, but getting to know the melody you want to play, is step 1. I guess singing/humming it, is the most easy way to mentally practice the melodic phrases and once it's in the brain, you can use that to start to play it on the instrument.
And indeed Greg, not thinking about melody, switches the hands into autopilot mode and lets the muscle memorized stuff come out.

Cheers,
Bas