I am not 100% sure about how many calls are made, but I would guess that there are at least 5: PID, IVs, Nature, Ability, and EC.
This obviously changes for wild encounters where there are more.
Since the maximum number for these calls is relatively low for most of the calls (25 for nature, 2 or 3 for ability, and 12 or so for encounter slots, plus level spread), the impact on unique spreads is low too. This includes full 32bit outputs like PID/IVs/EC.
Even if the number of sequential calls were enough to technically determine a contrived seed (which I am not convinced it is) it won't matter. It would take an impractical (50k+ super computers and months/years of time) amount of computing power to determine ONE spread.
I'll give you some more context as to how fruitless this is: You can capture pokemon every second for the rest of your life and have a near 0% chance of encountering a duplicate pokemon simply based on PID/IVs alone. If you include EC, it would never happen in 100k lifetimes.
To sum it all up, for practical purposes, you can get virtually any combination of PID/IVS/EC/Nature/Ability/Encounter for every RNG save seed.