IMO, no. You see there is always a power/knowledge imbalance. Even if you were to become friends with your T, your T will always more insight into you than you into her. Friends are usually on equal footing. One friend may have more insight about one thing, but the other friend usually has more insight about another thing. It works out. Your T has seen you at your worst.... you have never seen your T that way.

However, I do believe there are other relationships that are possible that are more, well, along the lines of the power/kmowledge difference, like parent/child type relationships that work out.