In short: no.
The link from newmediarights.org that PokemonLover222 posted is pretty good but I think he/she misinterpreted some of the facts there. (Also, that Yahoo Answers page is completely wrong as usual - never trust Yahoo Answers!)
A game with Pokemon in it is breaking the copyright of The Pokemon Company, simple as that. It makes zero difference whether the game is free or making money, if TPC don't want you to make that game they will send you a Cease & Desist order and get it removed from the App Store(s).
There is such a thing as "Fair Use" but that only applies to content used for "commentary, criticism and reporting", not games. TPC would claim that the game is harming their brand because it is unprofessional. Pokemon websites are largely seen as okay - we are just informational sites using a limited amount of pictures.
However, you can of course make your own game with similar mechanics to Pokemon, as long as all the creatures/characters are your own creation. There are already a ton of those games in the App Store (like that stupid dragon hunter one).