Yes - create a user account in your Do-more CPU that has Data Read access (not Data Write), along with Program Read. Anytime THAT user connects, they will only be able to read data. That user's privilege will apply on ANY comm port, i.e. it is NOT port specific, but SESSION/user specific.
You will probably want to make the "Default" user be data read/program read (i.e. Default User is the user with a blank, or no, password). Then have your "admin" or your user account (WITH a password), have full access (or whatever access).
See Help Topic DMD0259, Password Configuration for more details.