pdeeh,
The Ilford sequence (which I don't use, btw) is predicated on not letting the fixer soak deeply into the paper base. A short fix in strong fixer and immediate washing is what accomplishes this.
I voluminous enough water holding bath, with agitation, would accomplish virtually the same thing as a running water rinse, but stacking lots of prints in a regular tray is possibly not enough to prevent fixer build up and some of the (albeit dilute) fix from soaking further in to the paper base.
The only way to really know for sure is to test your prints for residual hypo (Kodak HT-2 test kit and comparison patches). It's a good idea to test your process anyway, for both residual hypo and retained silver (ST-1 test kit). If you can get acceptable results on the tests with your fixing regime, then you're good to go.
A couple of comments about the Ilford sequence: I find it wasteful of fixer. If you use a single bath, which is the most logical with such short fixing times, the capacity of the fix, when fixing for optimum permanence is only 10 8x10s per liter. Two bath fixing (30 seconds in each bath and then drain time...) invites exposing the print to strong fix for longer than the recommended 60 seconds, thereby allowing the fixer to soak into the paper more deeply, and possibly not wash out in the rather short wash time... And, Ilford has only tested its sequence on Ilford products, so other papers may react differently (e.g., soak up fixer more quickly than the Ilford papers) and require more extended washing. Again, only testing will get you a definitive answer for your work flow.
Personally, I prefer a sequence with longer times in two fixers, a water holding bath and then a treatment in HCA and a one-hour wash. If that's not practical for you, you should really make sure you test for both residual hypo and silver to arrive at a sequence that works for your materials and water-use and space requirements. The idea of a holding bath with HCA may end up just saturating the paper with sulfite, which requires some time to wash out as well.
Best,
Doremus
P.S: I crossed posts with David above; seems we're on the same wavelength