Can Kathy Griffin regain the career she once had? Sure…though the article I just linked to seems more interested in how much money she's made in the past than in how much she might make in the future.
I have no particular opinion of the lady as a comedian since I've never seen her perform live and I usually reserve such judgments until I do. But when I first saw her on TV, she was doing some pretty sharp, insightful (and funny) material…and I honestly don't know if she still does.
All I hear now is how she did some bit somewhere that may or may not have been funny but it was definitely shocking. Seems to me she needs to chuck the "how outrageous she is" routine and get back to the "how witty and funny she is," not because of political correctness or fear of reprisals but because I suspect people are forgetting — or never learning in the first place — how well she could do the non-shock stuff.