I wish my T would do something like that. I don't think he would, but it would be nice to have; I phone his answering machine sometimes but he speaks another language in that message so his voice is a bit different.

I don't think it would necessarily increase feelings of dependence to have a recording. On the contrary it might be a way to keep T "real" and lessen the anxiety around the breaks between sessions, and that might make you think less about them - perhaps.