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.