That would defeat the entire point of using a fingerprint to check the server's authenticity.
Think about it: you check the server's fingerprint against the known fingerprint. If a hacker tries to fool you by redirecting you to a fake server, the fingerprint is no longer the same, so you know that you shouldn't trust the server.
If you first get the fingerprint, and then check the server's fingerprint, they will always match, even if security is compromised.
You should use a CA certificate instead, if the fingerprint of the server changes.
https://github.com/esp8266/Arduino/.../examples/HTTPSRequestCACert/HTTPSRequestCACert.ino
Pieter