first of all, the cpu fan has nothing to do with the sensor for temp on the cpu. That is taken from a thermistor in the socket. The fan sensor will just tell you the speed of the fan and nothing else. You will find temperature from the cpu socket and mobo(as well as some vid cards now) and that's about it. The fan headers aren't really that useful except if you want to make sure that the fans are actually spinning at the designated rpm.
The four pin connector that you speak of should look like a molex connector(hd power supply, cdrom power supply connector, etc.) right? Then yes you would connect that fan directly to the psu but you will not be able to get the rpms from the fan then, which doesn't really matter a whole lot.
Especially with the new high speed fans, you will not want to connect them to the headers on the mobo anyway cause they will draw too much power and could short out your board.