I think Fred would take the care himself but let Serena die @kalapata
I know in the episode when she was shot he was upset and she was saved. But that was before.
I think now it would be all "it's god's will" for Serena, but he's not above breaking the rules for himself. He' would absolutely safe himself even if it meant a woman doctor.
Eventually it might even be convenient. She knows a lot about his secrets. He has more power now (ironically in part thanks to her while he was injured) and I believe she has become more disposable and a bigger risk all of a sudden.
If Serena did die, he could find himself a nice pliant Gilead wife like Eden and live off Serena's hard work which put him there.