For what it's worth, neither New Hartford nor Tacoma Guilds had the serial number stamped on the headstock.
The F-50 Standard was only made at New Hartford, and only between late 2010 and 2014.
The label in my '12 F-50 STD is just to the left of center inside the sound hole (treble side). If it had ever been there, there would still be a round area of glue residue about 2 1/2 inches in diameter where it had been applied. I can't imagine anyone removing it for cosmetic reasons (although there may be some players out there that consider them unsightly and remove them intentionally). And the chances of one that recently applied just falling off are remote, unless the guitar were subjected to high heat/humidity.
I have an '81 D-212 with an arch back that is missing its label (of course, it has the serial number stamped on the back of the headstock, so it can still be identified). Not sure if the laminated back contributes to a label peeling off.
By the way, My F-50 STD is just a wonderful instrument. It has a bass note that you can feel in your chest. Strongly recommended, if you can get some assurance that the one you are looking at is not hot.
Neal