The latest carrier based drones have airborne refueling capabilities just like the manned jets.
If you're talking about Northrop Grumman's X-47 UCAV, it is only developmental and has not yet flown off a carrier... But yes, drones having refueling capability, buddy refueling even more so, are going to set a new standard on mission duration.
But manned jets have to contend with pilot fatigue.
UCAV too in a sense : they are constantly monitored by one or two operators (sometimes even flight-rated pilots), who DO have to manage fatigue; the good thing is they are in a facility where crews can rotate without the aircraft having to provide accommodations for all those people. These aircrafts are unmanned in the sense that there is no man ON BOARD, but there is of course a man (or woman, one or more) in the loop. This is why they are sometimes called "remotely" piloted aircraft.
One of the latest tests off a carrier was a 55 hour non-stop single drone mission. There is not a pilot in the world capable of handling missions of that length. Even the existing manned B-2 bombers that launch missions from the mid-west to targets in the middle east are pushing the limits a pilot can handle.
Wikipedia states that a B-2 mission has lasted 50 hours with round-trip flight from Barksdale AFB to the Middle-East, but I cannot find any reference of it in the official U.S. Air Force website, which states that B-52s during Operation Desert Storm used to undertake missions of 35 hours. In both cases, these are bomber aircrafts which are designed for long duration missions : the B-2 has two pilots, is thoroughly automated, and of course has a toilet. Lockheed's U-2 Dragonlady pilots are not so lucky on their 9 hours mission (see http://www.blackbirds.net/u2/u-2mission.html) at 70k feet in their astronaut-like full pressure suit.