I'm no lawyer, but have been thru the FCC testing process a few times. For a ordinary device that doesn't deliberately transmit (called "unintentional radiator" by the FCC), there is no legal requirement for certifcation. There are legal requirements for what it is allowed to emit, but it up to you how to make sure your device works within the rules.
You can simply sell a unintentionally radiating device without testing. However, if someone files a complaint and the device is found to exceed the legal radiation limits, you're in deep doodoo. If you had the device tested by a accredited test lab and they determined it was within the limits, your legal case will be much better. The FCC still has the right to force you to withdraw the product and even confiscate every unit out there, but if you can show you followed accepted practices of testing then there will be much less of a issue of punative actions.
Intentional radiators are a different story. You do have to have FCC certification to legally sell one in the United States. When the device is certified, you get a certification ID, and that ID generally has to be indicated somewhere on the outside of the device where others can see it.
In the case of a bluetooth module, most likely the module vendor has gotten the certification for the module. If not, I wouldn't go near it. Even if so though, you are still on the hook for the product as a whole. The module will also be certified with some restrictions, like a specific list of antennas that it is certified with. If you attach a different antenna, for example, the module is no longer certified and you're on your own.
If you're trying to sell a intentionally radiating product, you'd better talk to a expert early in the process. You can wing it a bit with unitnentional radiators, but you really don't want to play games with intentional radiators, even if you're using a certified module that does all the intentional radiating.
It might be a good idea to talk to a testing house. They generally will know all the rules. Just keep in mind they sell testing services, and their answers may a bit biased towards you needing a lot of testing.
Best Answer
The only way I know to avoid the full FCC certification is to get a module that has an antenna already attached, whether an antenna connector, chip antenna or PCB trace. For example this Bluetooth module which I have used in the past comes with a chip antenna, in the upper left corner:
(I know you are using a GSM, but the same principal applies.) Note the FCC ID on the top of the module, this means the module has been pre-certified, because it has a chip antenna plus the relevant circuitry which allows the module to be tested as a whole. I have seen this even with modules that have an antenna connector, such as SMA or U.FL. Even with the pre-certification, you will have to go through some testing (to check, for example, that your microcontroller or other circuitry doesn't emit spurious emissions), but not as much.
The FCC doesn't care what kind of antenna you are using, as long as it passes the tests. I have never worked with a product that had a detachable antenna, but in that case, I imagine you would have to have something in your user instructions cautioning them not to attach an antenna with a gain more than such and such a limit.
Now in your case, the SIM800F module just has a pin that is to be connected to an antenna connector, or PCB or chip antenna. The datasheet for the SIM800F doesn't mention anything about FCC certification. So you will have to go through the more exhaustive testing.
One more note: if you have more than one radio in your device, such as cellular plus Bluetooth, or cellular plus BLE, etc. then all bets are off and you have to go through the full testing to make sure they play together nicely, whether the individual modules are pre-certified or not.