I think this would be a conflict of interest. It would take away time from the things you are obligated to do as a Nurse, however what you can do is put all those clinical hours you are working as a nurse on your AMCAS application.
Shadowing is done on your own time, purely voluntarily. It kind of sucks, but many of us in the non-medical field had to juggle, move our schedules, and use our precious vacation time just to get those shadowing hours. You are fortunate in that you have close contact with doctors who will probably have no problem letting you shadow them whenever you want. The hardest part for me was always finding someone willing to let me shadow.