No.
When the client sends something, whether it is P or H(P) or H(H(P)) anyone who intercepts this can simply resend the exact same thing, thus making any function like this equivalent to using the password directly.
That’s why you should use a nonce; The server can give out some random garbage k and the client will calculate H(P,k) and send it to the server. HMAC is a popular implementation of this method.
Provided the server never accepts the same nonce twice, this is secure against a replay attack.