The short answer is that Armenians are considered white in the federal race and ethnicity categories.
http://talk.collegeconfidential.com/...ssion-2-a.html
The long answer comes in two parts:
1) You can decline to self-identify with any etnnic group if you like. A lot of colleges admit a LOT of students who are reported to the federal government as "race/ethnicity unreported." The thread linked above links out to many Common Data Set reports about various colleges to prove that.
2) If you have specific identification with some unusual ethnic group and you feel that is an aspect of your personal background that you will to a campus community and will add to the diversity of the campus community, you may as well mention it. It may not help your chances at all, but it is hardly likely to hurt them.