Are you saying that if I didn't push, it would have eventually stabilized in a nose-down attitude?
Conditionally, yes. I will occasionally entertain myself on a very long, straight in final, trimming the plane flaps up/low cruise power, for a slight descent. Thereafter, I will aim to fly the remainder of the approach without pitch nor pitch trim inputs, while reducing power and extending full flaps incrementally. Remove a little power, nose dips. Add a little flap, nose rises, and airspeed reduces. This can be repeated without any pitch inputs, until you're flying with full flaps, and low power/low speed, on more or less the same approach path.
Though some Cessna POH's state that it is possible to actually flare and land without an elevator input, I've only once done this, while flying with a skilled safety pilot, who was about to take over and land, as I did not have my hands on the control wheel at all. Getting to the top of the flare with no elevator control is relatively easy, flaring not so easy....