PBC correction is necessary for analysis, calculations of rms, rmsf, distance, etc don’t account for the displacement due to PBC so not correcting for it will give you inaccurate results.
In the case of gmx distance, while you should definitely use PBC corrected trajectories when analyzing the data, I’ve actually found that sometimes the PBC-corrected trajectories would still not account for all PBC effects entirely (Atom to atom distance measured by gmx distance command is larger than measured in VMD), possibly due to some incorrect option I’d chosen for -pbc, so I usually include ‘-pbc no’ in the gmx distance command as well