I agree, electronic communication of any kind is sort of iffy, when it's between a T and client it is really fraught with peril. I didn't email my T until I had been seeing her over 18 mos, and even then it started very, very slowly. I didn't email her at all until she emailed me first.
The same with texting. I remember the first text I got from T was on my birthday, again about a year and a half into our work together. I'm not sure how it progressed from that to the point where we were having arguments via text, but I do know that with my next T I will be very, very hesitant to initiate or maintain any contact outside of sessions.

I'm not saying out of session contact is bad or wrong, only that for me it has created an almost unbelievable amount of heartache and confusion, quite possibly outweighing any good it did.