let's pretend that we don't have P just pK and we search random ranges to see if pK is within the range of some random valid range within Seco256k1.
No, we can't know the range of the private key by only having the public key. Searching random ranges also doesn't give us any information without actually finding the public key.
In other words if that were possible you could just look at any random public key, guess its range then limit the search space and brute force to find the private key.