".....I figure in park nothing should be moving in the tranny, except for the torque converter......."

And the pump. If the tranny was drained, at a minimum drop 3 or 4 quarts in it, before you start it. (Assuming it's a tranny like a TH350/400, TORQUE FLIGHT, C4 ETC).

If your going to run it for any legnth of time such as breaking in the cam, finish filling it as the warms up.