If you installed Win7 Family Pack on a fresh HD, then no, the installer will NOT take the key. Why? Because if you do a fresh install, it wants a full-version key, and not an upgrade key. You have to make sure that "MediaBootInstall" is set to "0" (zero) in the registry, and then do "SLMGR /REARM" from an elevated command prompt, and then reboot, and then go into Control Panel / System and enter the product key and activate.
As long as your hardware is the same as when you previously activated, then you won't have to call the 800 number. If the hardware has changed, but you haven't used all three license activations (over the internet), then you won't have to call either.