Trying out some stock cars (including tires, except where stock tires exceed restrictions) using level 25 Bobs (unguided) ...
Circuito de Madrid - Mini 400 PP (351-400 pp):
Isuzu Piazza XE '81 (351 PP, 135 hp, 125 ft-lb, 1190 kg) - 6:13 (8th)
Suzuki Swift Sport '07 (352 PP, 125 hp, 111 ft-lb, 1060 kg) - 6:09 (9th)
Peugeot 307 CC Premium AVN (354 PP, 144 hp, 142 ft-lb, 1490 kg) - 6:19 (11th)
Suzuki Swift Sport '05 (357 PP, 125 hp, 111 ft-lb, 1060 kg) - 6:11 (9th)
Honda CR-Z a '10 (358 PP, 124 hp, 131 ft-lb, 1130 kg) - 6:15 (9th)
Alfa Romeo 147 Ti 2.0 Twin Spark '06 (360 PP, 150 hp, 136 ft-lb, 1280 kg) - 6:05 (8th)
Mazda Eunos Roadster (NA Special Package) '89 (361 PP, 120 hp, 103 ft-lb, 940 kg) - 6:10 (10th)
Volkswagen Golf IV GTI '01 (365 PP, 151 hp, 157 ft-lb, 1280 kg) - 6:05 (9th)
Mazda MX-5 S-Special I (NA, J) '95 (366 PP, 136 hp, 120 ft-lb, 1000 kg, 6200 km) - 6:06 (7th)
Mazda MX-5 VR-Limited (NA, J) '95 (366 PP, 135 hp, 119 ft-lb, 980 kg, 65000 km) - 6:08 (9th)
Mazda MX-5 V-Special II (NA, J) '93 (367 PP, 135 hp, 120 ft-lb, 980 kg, 58000km) - 6:04 (9th)
Mazda Atenza Sport 25Z '07 (377 PP, 172 hp, 169 ft-lb, 1470 kg) - 6:01 (8th)
Spoon Spoon CR-Z (377 PP, 146 hp, 144 ft-lb, 1130 kg) - 6:00 (7th)
Volkswagen Lupo GTI Cup Car (J) '03 (378 PP, 136 hp, 123 ft-lb, 1010 kg) - 5:53 (6th)
Mitsubishi Lancer EX 1800GSR IC Turbo '83 (380 PP, 161 hp, 162 ft-lb, 1085 kg) - 6:09 (9th)
Volkswagen Lupo Cup Car '00 (381 PP, 126 hp, 115 ft-lb, 840 kg) - 5:50 (6th)
Toyota Celica XX 2800GT '81 (382 PP, 171 hp, 177 ft-lb, 1235 kg) - 6:05 (9th)
Alfa Romeo Giulia Sprint GTA 1600 '65 (382 PP, 115 hp, 107 ft-lb, 745 kg) - 6:09 (6th)
Honda Civic SiR-II (EG) '91 (382 PP, 166 hp, 118 ft-lb, 1040 kg) - 5:53 (7th)
Mazda 323F '93 (382 PP, 177 hp, 135 ft-lb, 1240 kg) - 6:01 (9th)
Alfa Romeo 166 2.5 V6 24V Sportronic '98 (383 PP, 200 hp, 171 ft-lb, 1520 kg, 12000 km) - 6:02 (9th)
Honda CR-X del Sol SiR '92 (383 PP, 173 hp, 119 ft-lb, 1100 kg, 45000 km) - 5:56 (9th)
Honda City Turbo II '83 (384 PP, 110 hp, 120 ft-lb, 735 kg) - 6:03 (7th)
Nissan 240ZG (HS30) '71 (384 PP, 156 hp, 159 ft-lb, 1010 kg) - 5:52 (5th)
Citroen C4 Coupe 2.0VTS '05 (387 PP, 181 hp, 154 ft-lb, 1330 kg) - 5:55 (4th)
Mazda Atenza Concept '01 (387 PP, 179 hp, 161 ft-lb, 1300 kg) - 6:00 (7th)
Marcos Mini Marcos GT '70 (387 PP, 77 hp, 80 ft-lb, 559 kg) - 6:29 (12th)
Suzuki Cappuccino (EA21R) RM '95 (389 PP, 71 hp, 82 ft-lb, 590 kg) - 6:31 (12th)
BMW 2002 Turbo '73 (390 PP, 171 hp, 180 ft-lb, 1080 kg) - 5:53 (4th)
Honda Civic Type R (EK) '98 (391 PP, 180 hp, 118 ft-lb, 1050 kg, 14000 km) - 5:56 (5th)
Honda Civic Type R (EK) '97 (392 PP, 180 hp, 119 ft-lb, 1050 kg) - 5:54 (4th)
Mazda Axela 23S '03 (393 PP, 178 hp, 165 ft-lb, 1260 kg, 1100 km) - 5:53 (4th)
Mazda RX-7 GT-Limited (FC, J) '85 (393 PP, 186 hp, 185 ft-lb, 1280 kg, 9800 km) - 5:50 (5th)
Mini Mini Cooper S '05 (394 PP, 170 hp, 165 ft-lb, 1180 kg) - 5:45 (3rd)
Mazda Roadster RS (NC) '07 (394 PP, 168 hp, 142 ft-lb, 1100 kg) - 5:47 (4th)
Nissan Silvia K's Dia Selection (S13) '90 (395 PP, 175 hp, 169 ft-lb, 1140 kg) - 5:51 (5th)
Okay, so no stock car that I have under 400 PP is able to win this (maybe the Mini Cooper S with weak competition), but I'd imagine that some of the cars with upgrades to 400 PP would be able to do it fairly easily, such as the Nissan 240Z, which ran a 5:52 on Comfort Soft tires stock and has 16 PP for upgrades and the Golf IV GTI, which also ran a relatively quick time (for a 365 PP) on CS tires and has plenty of room for upgrades.