No question they can.
I'd ask the Catholic parishes served by the married Protestant converts, and Eastern Rite parishes served by married priests in Europe, what they think of the dedication of their priests as well.
I know I keep harping on this Anglican dispensation, but I think one of the reasons it was originally allowed was as an experiment to see how married priests will work in a Catholic parish, and the guise of Protestant converts gave the Vatican the loophole.
Now that it's working so well, there's no logical argument that can be mustered as to why the Vatican doesn't allow married Catholic men into the priesthood as well. That's why the Vatican feels it necessary to pound the table every year, reminding Catholics that there will be mandatory celibacy (even if we can't really explain why).
This last proclamation, celibacy was an afterthought, tacked on to a larger discussion of the mention of Christianity's heritage in the EU constitution.