Is there a method to assign a tcode to a profile without adding the tcode to the Menus? Is this a matter of assigning the tcode directly to a user? This is a customer created tcode.
SAP prefers transaction code assignment occur through the menu screen on PFCG. However, you can assign them directly into the authorization S_TCODE in the profile view of PFCG. Once in PFCG go to the profile tab (dependent on version) click on "read old status and merge with new data". PFCG will present the authorizations contained with in the profile. You can then click on "insert authorization" enter "S_TCODE". PFCG will create an authorization for S_TCODE, click on the authorization to edit, and enter the transaction codes. Then generate the profile.
It is important to remember that this will not account for any ABAP authorization checks, only the initial transaction check will be satisfied.
You can not assign T-codes directly to users, you must assign them to Activity Groups/Roles/profiles and then to the user.