No, my T would never check in with me between sessions. I think for many T's any contact would need to be initiated by the client first and then a response would be something that may or may not happen depending on the T's boundaries and what has been discussed previously.

When I read this I initially thought I would love for my T to check in with me as it would show they had thought of me but actually I don't think I would. It could bring up some problems like others mentioned although I do think any problems could be discussed and worked through.