I think what Rafal wants to investigate is whether sodium sulfite will do some of the actual fixing on its own, thus making the wash-aid bath a kind of "mini" second fix. I believe he wants to single-bath fix and count on the wash-aid to take up some of the slack when the single fixing bath becomes exhausted. I.e., I believe he wants to use the fixer past its "for optimum permanence" limit and rely on the wash aid to get the print to "optimum."
There are some references (Ilford data sheets, etc.) that mention that fixing bath capacity can be "increased" by using a wash aid.
I would tend to be skeptical of relying on sulfite as part of the actual fixing process. First, the effect, if it exists at all, must be rather weak. Second, there is no way that I know of, nor any literature about, determining the capacity for a fixing bath using sulfite vs. not. Third, since fixer is much better at fixing than sulfite (if the sulfite does anything at all), it is simply easier and more secure to use the fixer to do the job and replace it as needed.
Single-bath fixing and optimum permanence means discarding the fixer relatively often in order to keep the dissolved silver under the limit for optimum permanence. Two-bath fixing allows much more capacity (approx. 4x) while at the same time ensuring that optimum permanence is achieved. Why substitute a proven procedure for a questionable and experimental one? Just to not have to make room for another tray? Or to save a couple seconds setting up and pouring in the chemicals?
A wash-aid has been shown to help in the washing process, especially for fiber-base papers, but it has not ever been in the mainstream as a fixer. There must be a reason for this; I'm sure Haist, Mees and many others would have recommended sodium sulfite for this purpose if it had been practical. I tend to conclude, therefore, that it is not.