You bring up a good point here! Not sure if it has been done yet or not, but it would be interesting to watch.
Closest thing I've seen was on the Top Gear show for the Star in a Reasonably Priced Car scenes. I always found it funny that the fastest Leader Board Times over the years were from, a professional motorcycle racer, a star that club raced as a hobby, and a couple stars that just preferred riding bikes.
I would imagine Schumacher, whom conspiracy theorists say may have been the Stig for a while, would do just fine in a stock car. The stock car driver in the F1 car however,
They had the F1 racers on a separate board all by them selves . From Wikipidia
All Formula One drivers are put into their own list with regard to lap times because of their exceptional skill level. When the Liana was pulled out from retirement to allow Jenson Button to make a time, Clarkson noted that the Liana would be pulled out for use by Formula 1 drivers in the future.
The original 'black' Stig and the first 'white' Stig have done laps around the track in the Suzuki Liana. Both had their times removed from the leaderboard upon their departure.
The first Stig was Perry McCarthy, who once test drove for the Williams F1 team, and drove for the ill-fated Andrea Moda Formula One team. The second Stig was Ben Collins; in the first episode of Series 13 the Stig was "revealed" to be Michael Schumacher, although this was a joke in the vein of the rest of his appearance on the show.
On 6 July 2011, Sebastian Vettel managed to top the board with a time of 1:44.0. Vettel's lap was the first time someone taking a 'Formula One drivers' line through the first corner was able to top The Stig's time, as Rubens Barrichello took the tighter line. Jeremy also mentioned on this episode that the current Stig has yet to do a lap of the track in the Liana, therefore there is currently no time on the board for the Stig.
The times and details of the F1 drivers' laps are as follows:
No. Driver Time Series Episode Notes
1 Sebastian Vettel 1:44.0 17 3
2 Rubens Barrichello 1:44.3 15 3
3 Ben Collins 1:44.4 The Stig II. (Removed from the board during interview with Vettel.)
4 Nigel Mansell 1:44.6 7 5
5 Lewis Hamilton 1:44.7 10 8 Wet & oily.
6 Jenson Button 1:44.7 8 8 Hot.
7 Jenson Button 1:44.9 14 5 Falling snow.
8 Perry McCarthy 1:46.0 The Stig I. (Not listed on the board.)
9 Kimi Räikkönen 1:46.1 18 7 Very wet.
10 Damon Hill 1:46.3 6 5
11 Mark Webber 1:47.1 6 10 Extremely wet.
12 Michael Schumacher DNF 13 1 Got lost at Hammerhead, and car was not seen again.