If I understand correctly, you have an external USB 3.0 harddrive connected to you computer and have not installed some drivers? If that's the case then you shouldn't need the AHCI drivers since AHCI is specific to the SATA-interface.
If it is a SATA drive you are talking about then yes, you should install the drivers, and no, it shouldn't matter wheter you have the drive connected or not. Might be more convenient to leave it plugged in if it is already so, so you don't have to open up your computer chassis.