Does the LHA generate enough power for one ? It's a good idea but I think about the power question.
Hmm ... the LHA could also use ice filled copper jacketed railgun rounds for close defense and short direct fire offense.
To be blunt, no. (but the DD(X) power system is very non-specific, http://www.globalsecurity.org/military/systems/ship/dd-x-specs.htm) But if it was a requirement, it could be done. It's big enough, with a flightdeck of 910 feet. A small reactor of the type used on LA class subs could supply power to at least 2 railguns at 12 rounds/minute, and supply power to catapults for the jets, as well as the rest of the ship. Sort of a twist, nuclear power for everything but the propulsion. ;)
The LHA sticks around in the area anyway as it has a hospital for the Marines, as well as helicopters for their movement when needed.
Sadly I think the USN brass is hung up on a super destroyer.