Well, yes, it does depend on those, as well as the amount of GFO and other factors. FWIW, I've spent many years studying phosphate binders in great detail with a large team of scientists as that is a big part of my professional job, so I'm not guessing, but there are so many things that impact the binding that one cannot give you a simple answer.
I think your idea of 'saturate' may be overly simplistic. The higher the phosphate level in the water, the more can be bound to the GFO, and the longer it is there, the more likely that other things will also accumulate on the phosphate binding sites (such as organics, etc). It is also reversible, so the phosphate can come back off if either something displaces it, or the phosphate concentration declines in the water below the point where the bound phosphate is in equilibrium with it.
In my tests, GFO exposed to substantial phosphate in seawater will reach equilibrium with it in 24 h or less. But if there is very little phosphate in the water, you may find that it takes a substantial period to occupy all of the sites, depending on the available phosphate in the water. If there is substantial phosphate, then it depletes the available binding sites rapidly.
