I could imagine it making sense if it created bubbles behind whatever it is that we're trying to clean (e.g. if the thing that's dirty is porous). However, that would not happen unless the bicarbonate made its way there, which would ~only happen if it was pre-dissolved, not added as a powder to vinegar (in which case you'd end up neutralizing it very close to the powder grains it's dissolving from). (Or am I overestimating the reaction speed compared to diffusion speed?)
Now this made me curious whether putting stuff in soda water under pressure, letting it soak it in, and releasing the pressure, could be a halfway sensible way to clean things.