Absolutely!
I prefer cove down. Haven't had much luck in getting people to follow along with me though. I clamp a couple small scrap blocks to the forms with a cutout in them to hold the strips. Drop the strip in the blocks, lay in a bead of glue, and set it into place. I think it's faster than trying to accurately place glue in a strip that's already attached to the forms and, like you said, you're not dealing with the sharp and delicate edges of the cove sticking up.
I did half a dozen or so canoes with the cove up before switching to cove down and doing a few more. I preferred cove down.
Like most things with strip building there are multiple ways to achieve the same goal and people successfully use them all. I don't like doing the same thing over and over again so it seems with every build I'd change at least one thing the build method. Some of those changes worked good and others didn't but they all resulted in a good hull.
Alan