I would definitely have assumed it was a weird spelling of 'carolyn'.
Sleuth, your pronunciation logic only applies if you're American (I guess?). Australians don't pronounce the 'o' in Carolyn, it's more of a schwa, so it's understandable to assume Karilyn was pronounced the same. We also wouldn't say 'care' for 'kar' in a name. EG, my friend Kara nearly always gets 'Car-a' from Australians and Britons, but 'kair-a' from Americans/Canadians.
Snuggles, if you really want the baby to be called 'Kari-Lynn' and not have to always correct people, then maybe spell it as it sounds. It's a made up name anyway, right?
Our friends' little girl is named Zara but you pronounce it 'Sarah'. I find that very confusing and can't see the point of spelling it a different way to how you want it to be pronounced.