The answer is, that marriage will not effect your citizenship (or in
other words, you will not be entitled to Latvian citizenship solely on
the basis of the marriage).
You can, of course, naturalise in Latvia regardless:
"Acquiring Latvian citizenship through naturalisation
Application to obtain Latvian citizenship through naturalisation is
received and reviewed by applicant`s local divisions of the
Latvian citizenship through naturalisation can be obtained by persons
who are registered in the Population Registry and
1. who at least five years (for persons who have arrived in Latvia
since July 1, 1992 the five year period is calculated starting from
the day their Residence Permits were issued) have permanently resided
in Latvia and who have reached the age of 15 upon the day of
submitting their naturalisation applications;
2. who are fluent in Latvian and are familiar with Latvian history,
fundamentals of Latvian Satversme (Constitution), and know the text of
Latvian National Anthem;
3. who have legal means of subsistence;
4. who have denounced their former citizenship and have received an
expatriation permit from their former citizenship country (if it is
required by the law of the respective country), or a different
document confirming their loss of citizenship. Citizens of the former
USSR who upon May 4, 1990 were permanently residing in Latvia have to
submit a confirmation that they have not become citizens of another
Children under the age of 15 can be naturalised along the same
procedure as their parents."
(SOURCE: Latvian Citizenship, <http://www.mfa.gov.lv/en/service/4727/>).
I hope this answers your question. Please contact me if you need any
clarification on this answer before you rate it.