According to Armenian Foreign Ministry, as of 12:30 9 August, there are no casualties among Armenian citizens in Georgia.
150 Armenian citizens in Batumi (Ajarian Autonomous Republic of Georgia) have been evacuated:
"Today, Armenia's Consulate General in Batumi organized return to their homeland of 150 Armenian citizens. Buses are provided with the Georgian police escort." More details (in Armenian).
Ajarian cities Batumi, Kobuleti and others are very popular and affordable summer holiday destinations for Armenians. I expect in this peak holiday season there will be thousands of holidaymakers from Armenia there, and in other parts of Georgia too. Along with the escalation of war between Georgia and Russia, more evacuations could be expected.