score:3
The EHIC card, that offers state-provided health care abroad is applicable only to Economic European Area, which is basically EU plus a couple countries. Georgia is not part of this set so you will not have any standard health care protection there (any form of health care at all actually).
But honestly, I am not sure mountain rescuing is included in any state-provided protection.
As @hippietrail wrote in his comment, you can rely on private insurance. Actually, you should check your liability insurance contract or ask them if they cover that case.
Otherwise there are some private travel insurances that are around 50 euros a month, for this matter (like World Nomads, AVI internayional, ...)
Reference : http://ec.europa.eu/social/main.jsp?catId=559