Yes, but accepting a foreign currency as your defacto currency is IMO insane. US sets monetary policy for the US and the US only. So if US raises interest rates to combat inflation that is occurring in the US. Georgia by default accepts this position regardless of what is actually happening in Georgia. If Georgia has deflation occurring, then this is bad for Georgia.

If you want to be a "Big Boy" country, you have to have your own monetary policy and currency. The problem is, managing your monetary policy and currency is really difficult. Countries that experience hyper-inflation are usually ones where monetary policy isn't done right. The other side of it is, when you do have the right monetary policy and currency controls, it allows to survive and possibly thrive in the financial world.

No country has adopted a foreign currency to make their central bank impotent.

The US Dollar is an accepted global currency for international trades.

So it kinda does make sense they accept it, since they can ultimately use it.