As a Catholic I can definitively say no, we do not worship statues.
Statuary and beautiful artwork are part of our tradition, and are meant to be powerful reminders of our God, our Savior, and the many who have worked faithfully in his service through two millennia.
Relics and bones are another matter. Sadly I do no some (mostly older) Catholics who are hung-up in something resembling worship regarding those.
I agree that this is not as much of an issue with the younger Catholics I know.