I say Yes. I still had to brace my 3 year old so his head wouldn't flop around. He has some core muscle tone issues and has a hard time anticipating fast movement in vehicles and compensating quick enough. He's 4 tomorrow, and it was only a couple months ago that he was finally able to ride without me keeping my arm around his shoulders.
A 10 month old would be similar, I think. There's a lot of quick lateral movements followed by spinning and sudden stops. I'd be concerned about strained neck muscles.
I see babies on it all the time, though. Makes me nervous...
If you do ride it, sit your baby in your lap facing out, and when the car is about to move, put your hand sort of over their face with open fingers, with your fingertips on his forehead, sort of "holding" his head in place. You'll know it's going to move when the game on the screen is over.