I would say most likely, but in reality there are more nuance to that. You could have a centered parameterization that contains pretty nasty geometric, but adaptation just ignore that and estimated the covariance around the mode. The result is that although you have a nicer geometry using a non-centered parameterized posterior (overall smoother and less curvature), it contains higher curvature around the mode and thus result in small step size after adaptation.
In general, so many things could happen it is hard to say what is the situation of your model. You could deep dive using e.g. the pair plot of the posterior sample for more insight.