I don't think this would work very well for me personally because I find that bringing my concerns back to my therapist (resistance, frustration, anxiety about the time between sessions, wildly fluctuating feelings about the therapeutic relationship, etc) enhances the connection and deepens my therapy. It's all a big, messy thing that ultimately pushes me forward. So I think the in-person relationship would be less rich if I were sometimes taking those thoughts and feelings to a third party. Sometimes I don't even talk at length about therapy issues with my spouse for the same reason. It defuses the tension but in a way that dissipates the energy away from therapeutic growth, if that makes sense.

It sounds like you and your T have a good understanding about outside contact. Do you feel like what you're currently able to do in terms of contact isn't enough to feel adequately supported? Are you well within your therapist's limits but still worried about contacting them too much? I guess I'm mostly curious about whether the online therapist could give you something that your current therapist can't.