No, if it's indeed the 004, a CVN, then there's no chimney. There's no feasible scenario in which a CVN needs so much auxiliary power as to necessitate a whole chimney.
The most likely explanations for the persistence of the chimney at the mockup site are:
a) It's testing two things at the same time. The island of the 004 and a chimney configuration for another project.
b) It's still under construction and the chimney will be gone when it's done.
c) The "chimney" is part of the inherent structure of the mockup carrier, i.e. office space.
d) It's not a CVN at all.