If we randomly selected a person from the US and assigned all non voter votes to them, would we see higher participation rates?

If you don't vote, your vote will go to Susan Smith, she's a 36 year old mother of three that works as a cashier at Family Dollar. We know none of her policy positions. Want to stay home and not vote now?

Bonus question: how many times would we actually see the random selection win before enough people got out to vote?