Not sure about Latvia but I'd guess it's not that easy. I'm sure there will be some form of residence requirement in Latvia. Why not search online or contact an Embassy?
I found this: "7) who have been married to a Latvia citizen for at least ten years and who have
permanently resided in Latvia for no less than five years as of the submission date of their
application for naturalization" here:
http://www.uta.edu/cpsees/latcit.htm
Please remember that this is an unofficial translation. I think there are also language requirements.
Obviously your residence (or PR) will have no ability to help you get Latvian citizenship.