GREAT IDEA. It is only logical. Since I write TONS of notes in Evernote.
When I write on my laptop and I need Grammarly, I use Chrome to write my notes. Then, once I'm done, I copy paste it to Evernote. Such a tedious process.
So yes, please integrate it.
Or if Evernote wants to use other spelling/grammar check tools like Grammarly, I'm also open for it. Evernote is AWESOME!