I voted for, 'Yes, maybe just a little...'
I don't think it's unlikely or farfetched; it's not unusual for kids that are close friends to have crushes on one another, after all. I know a lot of others here said that Nala seemed to be the one who had the crush mostly, but I always thought it was Simba! I think both of them might've had a tiny crush, but I always thought it was more on Simba's side than Nala's. Though considering that this Disney movie is so targeted to little boys (psh), it'd probably be mainly on Nala's side.

Regardless, I do think it's a possibility.
Oops, forgot to add: I agree that they might've had crushes but not even understood it themselves! I doubt they
really realized it at all, if they did crush on each other.