Yes, it would work.
This isn't exactly a worm gear on another gear but a somewhat similar application:
Frog Force (Team 503) used this concept on the their robot in 2005 and said they were quite happy with it. It seemed to work really well. Take a look at this picture:
http://www.chiefdelphi.com/forums/sh...&highlight=503
You can see the black worm gear shaft going down to the base of their robot under the arm. The CIM motor was mounted on the arm and is visible towards the top of the mast.