P element can increase its order on edge to get convergence automaticlly. With that you are able to get a convergence plot. For H element, I don't think you r able to plot it.
In ANSYS there is a possibility to plot convergence plot while obtaining results from non-linear problem. I'm looking for this functionality.
By the way You don't have to use automatic mesh refinement - P or H method.
I do not think that it can be plotted. But you can go to the msg file and look at the force residuals at each iteration. When the residual is less than a certain % of the average force convergence is said to have occured.