Hi, Kari! Great question and the answer is yes.
Any berry (except strawberries which are too acidic according to some) can turn into fermented preserves.
I shared a recipe here:
http://gnowfglins.com/2011/07/08/fermented-raspberry-preserves/
You'll need Pomona's Pectin, an alternative pectin that doesn't rely on sugar to set. These preserves are not totally gelled like you expect with today's preserves, but they're still delicious. We eat them on toast, stirred into yogurt or kefir, and yes, you can use honey (or any sweetener you'd like).
We picked blueberries last week and I'm going to make some blueberry preserves just like this...
Enjoy!
--Wardeh ('Wardee') Harmon
GNOWFGLINS -- Enjoying "God's Natural, Organic, Whole Foods, Grown Locally, In Season"
Author of "The Complete Idiot's Guide to Fermenting Foods"