Can I steal a neutral from another fixture on the same circuit?
So, given the comments, although electrically this would work, it is unsafe and a code violation.  This is because the hot and neutral are to be in the same raceway to have the magnetic field of the hot wire cancel out the magnetic field of the return wire, and thus reduce any induction eddies in any nearby metal components.  Such eddies could cause heat buildup and be a potential fire hazard.
It has also been brought to my attention that the dimmer that I had bought has no electrical safety standard certification such as CE, CSA or UL (or anything else for that matter).  FCC is a radio emission standard, not a safety standard.