As I understand it, spell check is handled on a system level. Evernote itself does not have a spellcheck function. That does not make it OK, but, this may be a case of he said she said between iOS and Evernote. In the end I don't care. Spellcheck is a basic function of writing and it's rediculous that it is not being addressed, especially with all the silly unwanted features being showered on users and so many alternatives out there.
Adding to this: Spellcheck still completely broken on an iPad 4 iOS 7.1.1. According to this thread, it's been broken since last Spetember. According to iTunes in that time there have been 13 application updates and exactly zero replies from Evernote. I love this product but really, this is unacceptable. I will not be renewing my subscription until spellcheck is fixed.