Red Bull is already involved in the Pikes Peak Hill Climb. They support both Loeb and Millen, the top two car drivers this year.
Red Bull Pikes Peak News
And i'm not sure if a F1 car will be faster up the road because Pikes Peak is not an usual smooth race track and has narrow turns that are difficult to take for a F1 car. The 208 of Loeb has more power than an F1 car, i would guess the same amount of downforce or slightly more, very wide tyres that provide grip, very short gear ratios that allow a top speed of 240kmh and a well prepared suspension that suits the track. The only "negative" point is the weight of 875kg, more than 200kg above F1 level, but weight isn't everything in racing.
Acceleration numbers are (
source):
1,8s for 0-100 kmh (better than F1!)
7s for 0-240 kmh (similar to F1)
Dear FIA, if you read this, please pm me for a redesign of the Technical Regulations to avoid finger nose shapes for 2016! :-)