Sodium sulfite sort of helps uncover development sites on the grains and can help increase film speed; it doesn't take much. For example, HP5+ in Rodinal 1:50 gives EI 200, but with the addition of 20g/L sodium sulfite the EI increases to 320 for the same CI.(posted 8977 days ago)Larger amounts of sodium sulfite acts as a solvent, nibbling away at and smoothing the edges of grain clumps (the "grain" you see) but this has the effect of decreasing acutance.
I can't think of anything that sodium sulfite could do to let anyone increase development time other than work as a preservative; that might allow a longer time with a developer that otherwise dies due to oxidation during development. But if the point of a longer development time is to increase contrast, a simpler solution would be to use a stronger developer.