Probably not, but that's something to address.
What I see is when the TCC behaves normally you get good idle. When it's not slipping like it should the controls fight to keep the engine alive and cause surging.
You said it gets better when the transmission warms up. That means thinner fluid and tolerances open up to reduce friction. Something is dragging, and there's not much in there to do that other than the clutch and a couple bearings.