Only if she's the type. Many women, for better or worse, will NOT be happy to hear this and will silently freak out, assuming the worst.
1) that's an idiotic stereotype. Men and women both will react in similar ways.
2) Doesn't make a difference what "type" of person she is. They are married and she has every right to know (and voice her opinion on) if a big part of their financial future will be impacted by him feeling burned out. Hopefully she'll be supportive, but either way she deserves to know the truth.
Great relationship advice.