I think there are two different types of “Catholic media” — the old guard liberal dissenting media, e.g., National Catholic Reporter, America, Commonweal, v. newer more orthodox media, including EWTN, various Catholic blogs, etc. Only the dissenters I would think would have the strong Democratic party ties.
The lines are fuzzier than we'd like to think. From the National Catholic Register, written by it's former editor-in-chief:
Time for True Democrats to Start Their Own Party [or, why Catholics can't vote Democrat any more]