It is a legal requirement? Yes (or as stated above - a visible indication, usually on the dash).
Would anyone ever pull you up on it?... Unlikely
Despite towbars being part of your MOT nowadays, the electrics aren't checked (other than a visual inspection of the socketry, wiring and towbar mounting points etc), so again this shouldn't be an issue.
However, all that said, I do like to see that my indicators are working, when I'm towing
Requiring the plug shouldn't have affected the vehicle electrics. Open up the plug again and just check you've got it wired correctly.
Pin 1 Yellow left indicator
Pin 4 Green right indicator