I would love to.
Regarding the story though:
1) Open to the elements shouldn't be a problem--just like riding in a convertable. (and some biplanes do have closed cabins)
2) I (along with most people that fly) generally don't fly with a parachute now.
3) Why would a pilot be any more likely to be intoxicated because it's a biplane? (besides, I would hope to pilot the craft myself)