no, it doesn't have anything to do with the similar sounding name of a beet soup.
Well, yes, it does, more than you might think! ;-)
It seems to be a curious innovation of the translators
Not so curious an innovation as you suggest, after all.
A "boustring(ue)" is a pickled herring in the dialect of Brussels, made to look "Russian" by adding an "–ovitch".
Whilst this joke would have been obvious to his readers when it was first published, it doesn't carry over into English - it probably doesn't really play outside Brussels!
So the translators took the opportunity to make another, different, food-related joke - "Borscht's off!" being presumably a play on the "Soup's off!" cliché, used to say a meal is over, or that the kitchen is closed, which the English reader could
It actually pairs quite nicely in the original with "Wirchwloff" (who became "Vlipvlop" in English).
His original name is another
food-based play on words, this time "witloof", the name of a kind of chicory, popular - and produced - in the region around Brussels.
This time a food reference seems to have been beyond even Michael Turner's legendary skill with matching Hergé's puns, but "Vlipvlop" is of course a "Russian"-ized version of "flip-flop", used of a spy turning from one side to another, or in this case going from disguise as an innocent bystander to exposure by Snowy, so he still got a good gag in in its place, I think.