Hard to say without knowing exactly what you have but most hydrangeas will tolerate part shade or even require it in your neck of the woods. Especially if it's one of the macrophyllas - the type most often sold at large garden centers. When does it get out of the house's shadow? Late afternoon? If the area gets a good amount of indirect light ("bright shade") chances are they will do very well there.

It will definitely get bright filtered shade (due to the pergola overhead), I had some peace lillies there in large pots, that did OK, not great, it was still a bit too hot outside for them. But they lived there quite a while anyway.

I also have some ferns there (inground) that come back every year and some hosta, also happy there. I was thinking maybe to give them a trial run, I'd leave them in containers and see how the summer goes, and plant them if it all looks good.

Another consideration is to oover a small section of the pergola that is near the roof line and that would create a foot or two of direct shelter, and even so, they would still get a good deal of filtered sunlight. I have NO large trees on our property...so it's hard to find true shade ;)

In Georgia they will want protection from the hot afternoon sun. Any sun in the morning - even full sun - should be fine.