Correct in principle, but not in practice. My implication was that you have to be very careful about what steps you take. Fixing some atom coordinates or using positional restraints will certainly change the outcome. Translation and rotation can be rigorously removed, and often are after the fact; that's not the same as fixed atom constraints.
There is a command to keep a protein, etc. centered (see the end of dynamc.doc), but that does not remove rotation. (It also does not support atom selection, and can only be applied to atoms defined first in the PSF.) I don't think there is currently any feature in CHARMM that will periodically re-align the molecule during dynamics. It would certainly make the dynamics somewhat slower to do so, maybe a lot slower.
The system you've described, with a long axis, is highly anisotropic; I don't follow what you mean by the isotropic comment.