No, the SL-7s would make lousy command ships. They're not terribly reliable, not designed to house people, and probably larger than is really necessary.
Speed is not a compelling requirement for command ships. Since they travel with the fleet trains or amphibious forces anyway, a speed of 20 knots or so is perfectly adequate.
PS: I note that apparently JCC(X) is not quite dead yet. he Navy is apparently looking at adapted LPD-17 hulls for the role, beginning in the FY12 budget. This strikes me as a sensible idea -- LPD-17 is well designed for damage control and should be adequate in size (two of the four existing command ships are converted LPDs of older designs significantly smaller than the new LPD-17 design).
http://www.fas.org/sgp/crs/weapons/RL34476.pdf