Yes, it can … or rather, it can, if you manage to take off without a catapult … the F-16 simply doesn't HAVE a catapult mechanism ! You can try to takeoff without it … if you succeed, well, then, it CAN takeoff from a carrier, else it can't !
Although the Viper wasn't designed for maritime operations, there is the possibility to start from and land on a carrier. You can toggle the arrester hook with Ctrl+H.
If it is not correct, please edit someone that wiki article.
The F-16 does have a tailhook (the real thing can be fitted with it, it has purposes other than naval aviation) and that would work on a carrier, but it still has no catapult mechanism.
Conceivably you can hit the AB with no payload and low fuel loadout and have a chance to make it in good winds - not all that useful, but here we go.