Yes, depending on your destination (i.e., if the particular firearm is legal where you are going).
Routes have to be planned very carefully to avoid stops and/or change of flights (where you take possession of your own luggage) in places that may not allow that particular firearm (as in the case of ARs in California).
In my experience, it is a speedier check-in. Gun unloaded, magazine empty, in a locked hard-sided case that meets TSA regs and with TSA approved locks. At the checkin counter, request to see a TSA supervisor (not just any clerk). Inform supervisor you will be checking in a bag that contains a firearm. Go back behind the counter, bags physically inspected, and gun inspected. I have always put ammo in the box inside the same case as the gun. They used to put bright orange tape that says CONTAINS FIREARM on the luggage, I am told they either do not do this anymore or do it only sporadically. Then you get your boarding pass, and proceed from there.
If you have a firearm on you (on your person), your credentials are inspected at the same time as the bags. Then you are escorted thru the screening point (where they turn off the metal detector for you to pass, so it does not beep and alarm other passengers), and go on your merry way. It helps to have the "Advance-to-GO-and-collect-$200" card
At larger airports, you are escorted past the screening area, joining other passengers post-screening via a different access route. It is also this way on international flights.
I am told the primary flight crew are informed of your presence, and your seating assignment. I do not know this to be a fact.