It depends on the individual therapist most likely and both their views/approaches and their own personal life demands. With one shrink, I really only had access to a service in case of crisis. He was good about calling back and didn't seem to mind.

With my current shrink, he likes the contact, but he limits it to a brief response. If it goes longer, then I have agreed that he can charge me, which is only fair. Since the therapy we do includes being honest and self-disclosing, he lets me know what is going on with him so I know whether or not the timing is appropriate. Over time this out of session experience has taught me a lot because I have learned that he is a human being after all with his own life and things to deal with so the relationship has become more real, which has had all kinds of benefits.