Welcome, Hi-Potter,
Yes that makes a very nice (a little expensive)installation, but you'd better put a switch in that W/P Extension Adapter.

Unless the wH came with the cord, I don't think that it can be connected this way.
All bathroom recps require GFCI protection, but no receptacles are required at all in this bathroom.

On another note: That water heater and the added plumbing under the sink sure make it ADA ngerous place for any one in a wheelchair. [Linked Image]