I think it would be a stellar battle. He wouldn't give a shit she's a woman.
"Who cares. She's incapable. Her credentials are flying around visiting countries on a government plane. She said so. Big deal. I've been doing that longer, profitably, and I pay my own way."
She'd cry to play the 'woman' card, and he'd say, "Did you cry about Bengazi? No. You said 'what difference at this point does it make.' lose the alligator tears."
He'd slaughter her on principle alone. he was ruthless to Rosie Odonnel. He'd have enough material to have a reality show with HC.