I think most wouldn't be that interested if there wasn't an actual driver (in the car, too, not some remote thing), even if it's ultimately faster.
You'd have teams in "pits" monitoring their vehicles live. Those reactions will be raw and humanistic.
When the vehicle comes in for a "pit stop," the team--in addition to doing mechanical maintenance--could be allowed to tweak the code, e.g. based on strategic observations of other cars' behaviours. To keep it interesting, one could mandate--to make up for the electronics in the car--all "pit stop" labor be completely manual. (Any code changes could be taken onto the track on an unpowered drive.)
This would not change for me if it were AI's with identifiable characteristics doing the activities (driving). With suitable marketing maybe real sportsfans could get behind (hypotheically) Team Waymo's AlphaRomeo Zero. Especially with an e-sports tie-in. Imagine racing, and thereby helping to train your (AI) hero on a simulator.
I do agree that such a class could be run along side a human-driven class as an alternative event. To go one step further, I feel this is where the Red Bull Air Race should go, so we can see some actual jet-powered racing at ridiculous speeds.