It is not ideal to expose the core, but it is a closed cell foam so it will not soak up water. It will however not be very strong on the edge as there is very little material either side of the core, any impact will damage the edge quite easily.
The main issue is the balance and stability of the blade through the water. Yes you can paddle with it but to get the best stroke it might be difficult as the blade will want to track differently in the water to what it is designed for. Also the thick edge will make quite a splash and noise on entry to the water, not matter what you do this will not go away which could be frustrating.