The answer to your generic question is "it depends".
Truly random encounters (csprng for every call): no correlation
Random-enough encounters: no correlation -- examples are gen5 wilds that use a 64-bit RNG but only have 32-bit PID, nature,gender,encounter rolls
Somewhat-random encounters: correlation. can figure out an RNG seed quickly (Tera/SWSH raids), or via bruteforce (shiny dynamax adventure raids, PLA captures, BDSP breeds)
Others generate with fixed data (like HOME gifts), and must match what the encounter requires.