Yes. Their corporate policy - not law - says
"You must ship your packages that contain handguns with UPS Next Day Air Early A.M.®, UPS Next Day Air®, or UPS Next Day Air Saver® services"
More at
http://www.ups.com/content/us/en/resources/prepare/guidelines/firearms.html
You might do best to print out the page and take it with you, some clerks will try to deny you or to rip you off. Note especially the line that says:
"between persons not otherwise prohibited from shipping firearms by federal, state or local law and when such shipment complies with all applicable federal, state and local laws."
and the part out of the BATF FAQ that says:
(B8) May a nonlicensee ship a firearm by common or contract carrier?
A nonlicensee may ship a firearm by a common or contract carrier to a resident of his or her own State or to a licensee in any State. A common or contract carrier must be used to ship a handgun. In addition, Federal law requires that the carrier be notified that the shipment contains a firearm and prohibits common or contract carriers from requiring or causing any label to be placed on any package indicating that it contains a firearm.
[18 U.S.C. 922(a)(2)(A), 922(a) (3), 922(a)(5) and 922(e), 27 CFR 478.31 and 478.30]
Air shipments are checked in and out at every stop which reduces theft by their own employees. It is just coincidence that they make more money off airmail.