Nintendo is very methodical when buying development studios. They like to work with them first, make sure they 'get' Nintendo's philosophy and then maybe acquire them.
EA would be a massive problem and distraction for Nintendo.
Aside from that, but EA's Sport licenses like NFL are specific in that EA has to make them for all consoles and that would still be enforced even if Nintendo bought them.
There's simply no way Nintendo would buy out EA. Too many problems, too few studios that would 'get' Nintendo's ideals. However if EA goes bankrupt Nintendo could pick up a few of their studios. Bioware maybe, as that's an area Nintendo needs help in (WRPGs) and Bioware makes top quality stuff. There's more to Nintendo's ideals than just quality but it would be a good working base to start from.