If the sear does NOT have a serial number, you can automatically rule out it being the registered part.
The form 4 could say machine gun but the registered part could be something else. Ive seen plenty of M1/2 carbines like this (operating rod or trigger housing stamped with manufacturing and serial number) If the form 4 serial number matches the receiver serial number than that's a registered receiver and not another part.
Obviously, if the receiver takes a permanent modification that ATF says is No No then the sear could be (so called) married to that receiver.
I would suggest looking at BOX H on the form 4 it might shed some light on it.