Can a woman contract urethritis from giving oral sex to a man who already has it?

Not possible, but...: STDs don't travel through the body. Infection occurs only at exposed sites, so there's no way you can get a genital infection from such an exposure. However, your throat can be infected by some causes of urethritis, especially gonorrhea. Both you and your partner should be avoiding sex entirely, oral or otherwise, until you both have been treated for this STD. You need both testing and treatment.