Hi Scarlet. I think this is a great idea. In my experience I find it very helpful.
I actually think for me I would just record the start of the session, and keep recording for a certain amount of time. I find that I very quickly forget that I am recording. But if you were trying to record a specific subject then you or T might be kind of speaking to the recording rather than each other and might feel less natural? IDK that's just my thoughts. Anyway I find it super helpful to have a recording and listen back. I hope it will be helpful for you too.