My experience:
I often leave prints in a clearing bath for up to 1/2 hour or so before the wash with no problems (e.g., the washer is already full). The problem with leaving them for really long periods of time (hours) would be emulsion softening as mentioned above. That said, I would try it and see. If your times are short enough and/or you get the prints to the washer without damage, you should be fine. If you can, however, try to give the prints a rinse before placing them in the wash aid in order to avoid build-up of fixer in your wash-aid bath from carry-over.
The sulfite in the wash aid will not damage your prints with extended exposure. The softening effect only goes to a certain point; handling may be an issue though, and try to keep your times as short as possible. The sooner you get your prints washed, the better. Do a residual hypo test after the wash to check your workflow.
I would think that adding the wash-aid bath to your workflow would be an improvement assuming you are just using a water holding-bath at the moment.
Best,
Doremus