They would probably live, but I doubt they would get tall enough to cover the air conditioner.

Plant yourself some Stuttgart. It's a very nice canna and they need a little shade or they'll burn.

Buy the old fashioned varieties...the ones that get 10 ft tall. They may not bloom for lack of sun, but they will grow. Also look for the varieties grown mainly for their
foliage, the blooms are incidental. I have one in full shade...almost 12 ft last summer... very exotic...needs lots of water and fertilizer! They may not like the "wind" the air conditioner produces...the leaves may tear and look ragged.

Last year I planted a canna, and this year it has 5 shoots with very healthy leaves. I am unsure exactly of the type of Canna (typical one with red flowers on a stalk), but it is growing very healthy and it is in part shade. It may get a little afternoon sun, but that is it. It is way healthier than any of them I have ever seen for sale. The leaves are also larger than any of them I have ever seen for sale, and this includes the local Amish grown ones. I think its just right place right time with some of them.