That is one of the issues with new T and I. New T said he checks texts and emails twice a day and it is OK to send him messages, but he might not get to them. He charges a prorated amount for phone calls. But then he got angry that I messaged him. he said he set a boundary about it but he didn't, at least not a clear one. So now texts are simply scheduling and emails have stopped. I can be OK with that, especially if it helps us work out the other crap he and I have been dealing with.
Awesome T let me call, text and email as much as I needed. It ebbed and flowed... sometimes it would be just one message to let him know what I got from our session... other times they would be almost daily. He never promised to get them all read before session but usually he did. Often he would reply. BUT there was NEVER any resentment or strings. That is essential for me... if you are going to offer me something then no resentment or strings.
I think I relied on the messages with awesome T too much... I didn't need them but they became a comforting habit. I miss them. I was trying to create a different habit with New T and not message and I had been doing well... clearly not well enough for him.
So, for me, outside contact and if it is good for me or not depends on the therapists ability to keep it safe... no resentment, no strings.