I think it's pretty cool that you feel close to your T. I have similar issues with not being close to people and keeping everyone at arms length. For me, it's automatic. I don't even know how to be close in the first place and it's like I don't even know who I am. I can try with people but it's like something doesn't fully attach in me. Like I'm broken somewhere inside. I would like to be able to email my T but he hasn't said I could. The couple times I've done so, they have been brief and disclosed my more positive feelings that don't seem to appear much during sessions, unfortunately. My T seems really glad that I've sent them......
To you, I'd say go for it and let him be close. Dependency isn't bad - especially since it's what your working on in the first place. But I can't practice what I preach

I don't know how, really. Sometimes I feel like my T and I almost start over again each session, to some extent. Your relationship with your T sounds awesome