They may not be all that happy in that situation. There are a lot of variables though that may make things better or worse than the average west-facing foundation scenario. Multiple soil-type variables, how much you water, how you mulch, what type of siding you have, and who knows what else, will all play a part in how well your hydrangea will preform. They are best used in an area where they got morning sun and evening shade with well-draining, moist soil.

As Brandon said, there are lots of variables. I've had very good luck with Lady in Red Hydrangeas on the west side of my house. They are planted next to red brick, which retains a lot of heat. In fact many sun/shade plants, like columbine, canna, wild geranium, azalea, do very well in that location. Almost all of my hydrangeas stress in the afternoon with the relentless heat and then perk up again around 7 pm. Established plants can handle this even though it doesn't look so great. If you're putting in new plants, give them lots of water. My Lady in Reds are really fast growers and they do not stress. Not sure if it's the west foundation location or characteristic of the variety.

I have a reverse questions about Annabelle...will it do well in dappled to heavy shade all day (i.e., no direct sun to speak of)?