Long answer: Sure, you can download APKs (android application files) if you find one on a website, but you cannot install or run it on a Windows Phone.
Sorry, I misinterpreted your initial question. You can add your Gmail account using IMAP but that limits your functionality somewhat. MetroMail is reviewed as a good way to handle Gmail on Windows Phone as well. But the answer is that there's no first-party (ie, from Google) support for Google accounts on Windows Phone.
Also, this is an Android specific forum. There is a sister forum that covers Windows Phone.