Email can provide a good enough timestamp for the file, proving that you were (or rather your account was) in possession of it at that time, assuming that you can still log into the account to see that. Given that the email server is hosted by Google, there is next to no chance that you would have been able to tamper with the timestamps on their end, and I don't think it's possible to edit your document after the fact. Still, it's not the same as what a timestamp authority does because it's not secure cryptographic timestamping.
Of course, if your purpose was to be able to take someone to court for copyright infringement, then it won't help you. Neither will anything similar: this is called a "poor man's copyright" and "there is no provision in the copyright law regarding any such type of protection, and it is not a substitute for registration" as the US Copyright office tells you. They'll also remind you that you cannot copyright an idea, only your specific depiction of the idea.
You owned the copyright to your words the second you put them down. But you only gain a number of legal protections when you register your work for the price of $35-$55. According to the American Bar Association:
An author cannot bring a lawsuit for copyright infringement, however, without a certificate of registration from the Copyright Office. [... U]nless the application for registration of copyrights is filed with the Copyright Office within three months of first publication of the work or prior to infringement, certain valuable remedies are not available to the copyright holder—including the right to receive statutory damages up to $150,000 per work infringed, attorney fees and costs, injunctions, and impounding and disposition of infringing articles.
The difference between statutory damages and other damages is important: there are many cases where those other damages will amount to nothing. And if you didn't need attorney fees to be covered then you had more than enough money to get a proper registration in the first place.