Yes! As noted in the answers to FAQ #1 (“I Live Outside The U.S., Am I Eligible To Vote In U.S. Elections?”) and FAQ #3 (“Can I Vote In State And Local Elections?”), overseas voters may vote in all federal elections and may also be able to vote in state elections.
A Primary Election (usually held in the Spring or Summer) is used to pick the party’s candidates who will compete in the General Election (usually in November). If you are eligible to vote in the General Election, you are eligible to vote in the corresponding Primary Election. Keep in mind however, that some states hold a “closed” primary–voters must declare their political party affiliation to receive a ballot for the Primary Election.
VoteFromAbroad (VFA) will assist you in filling out and submitting your Federal Post Card Application (FPCA) to your Local Election Official in the U.S.–and will prompt you to declare a political affiliation if required to vote in your state’s Primary Elections.