Do Armenians consider themselves Russians?

There was only one Soviet Union; there were no "soviet unions".

Even when Armenia was one of the constituent republics of the Soviet Union Armenians didn't consider themselves "Russian". The USSR itself wasn't "Russian", although the Russian Republic was the largest of the constituent republics and the capital of the USSR was in Russia and Russian was the lingua franca among the 15 republics.

Of all the peoples making up the former Soviet Union the Armenians - and the Georgians - were among the very last to tolerate the idea of somehow being "Russian".

Only if they live in Russia

I'm Greek and I have family in Russia too

There are two ideas about national origin in Russia. Like this, as exact as l understand it. Nationality Russian, ethnicity Armenian, if living in Russia with a Russian passport. 

This can apply to other countries as well, Mexican ethnicity living in USA as a USA citizen. 

In Russia, this may or not be listed on passports now. I'll find out when l receive mine.

No, they don't. They consider themselves Armenians.

They've been Armenians since 860 BC. 

No... why would they 

Do Canadians consider themselves Mexicans?