Hi Stevega,
I don't know why they wouldn't. We always think of them being attracted to red flowers, but they also like my lavender, russian sage, catmint and globe thistle. Even flowers that don't have a lot of nectar might still have the tiny insects they eat for protein. But I'm pretty sure caryopteris is a great nectar plant given that the ones I tried were always covered with bees and butterflies in fall.

I'm just envious that you can grow caryopteris - I've tried (2x) but it doesn't make it through the winter and it's such a nice late season bloomer.

Yes, they do like caryopteris.

Lucy, some are more hardy than others. We are at a new house so I planted one this spring. It was supposed to Petit Bleu which is a small variety but I clearly got the wrong one and will have to move it next spring. Way to big for the space where I planted it! The same place also sent me the wrong butterfly bush.....