that video title...no they wouldn't...Any time I see a guy fighting a girl I always think back to doing training where the goal is advancement not murdering the other person.
We had a Co-Ed training block and the one time I was paired with a girl for grappling it was the most awkward fight ever. She was fighting for her life and I was trying to not leave with a restraining order. Holy shit she clawed the fuck outta me too. Like the fuck am I supposed to do, beat the shit outta some girl on the mat? Who does that benefit? She gains nothing because there is no way for her to physically fight me and I gain nothing because I have to hold back from actually fucking hurting her.
This is what grapling a girl looks like...
You are constantly looking around for someone to basically stop you from doing what you would do to ANY guy.
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EDIT:
The double awkward part is you are basically dry-humping one another on the mat. Which is...interesting...