I suppose it is possible, only if both (fan and performer) feel the same way. If it's a question of only the fan "thinking" they're friends, then you're getting into Eve Harrington territory. Speaking personally, I'm a social media friend/acquaintance of a few cast members of my favorite show. The brief moments we've spoken/chatted have been at the theatre in question or on FB. As a result, I have been able to visit backstage on a couple of occasions.
"Noel [Coward] and I were in Paris once. Adjoining rooms, of course. One night, I felt mischievous, so I knocked on Noel's door, and he asked, 'Who is it?' I lowered my voice and said 'Hotel detective. Have you got a gentleman in your room?' He answered, 'Just a minute, I'll ask him.'" (Beatrice Lillie)