That's right. A suppressor is actually treated as a separate 'firearm', regardless of whether it is built integrally into the host firearm or as an independent device.An integrally suppressed rifle is a good example. It will have two S/Ns as well. One on the rifle, one on the suppressor.
(and yes, the ATF considers a suppressor to be a 'firearm' legally, despite the fact that it can't chamber or fire a cartridge on its own).