No... he had an extra Pokéball since he had captured FIVE Pokémon prior to that, and Pikachu is off the ball 24/7.
Anyway, I'd probably do a lot the same... except that as soon as I got to a new region, I'd find the closest computer and look for information on the Gym Leaders, spoilers be danged. At the very least, I'll have my priorities straightened in case I happen to find a powerful Pokémon which I know can help me later, which in Ash's case inevitably happens.
I'd probably see if I can't ask people for cooking books, even if it's to drop it on my companions. Hey, you can't live on an empty stomach, can you?
Oh, and I am pretty sure everyone here agrees that, no matter who takes Ash's place, there's a better chance of said person not being... um... I'm not remembering the word right now, but the point is that you'd probably make a strategy instead of rushly using the same move over and over, without a pause.