The tang on the wooden handled Mora's tapers down in a couple steps and does reach the end of the handle. In a strict sense, I would define "full tang" as the blade steel extending all the way to the end of the handle, with close to the same thickness and width as the blade. The handles on a full tang knife are typically slabs of material (scales) that is riveted or screwed in place. Some modern variation have the handle material molded on.
I see batoning as a marginal technique when using a knife, and particularly with a small blade. It is fine if done with care and discretion, but you could find yourself without a cutting tool when you break your blade-- a bad thing if you are in a situation where you need it to survive. I would baton wood with a diameter that is about the same as the depth of the blade, leaving plenty of blade length for striking.
My hunch is that most breakage occurs from prying and twisting movements in an attempt to complete splitting a stick. Making small kindling and getting to dry inner wood for fire-starting is good, but I would stay away from the heavier stuff, leaving that to a light folding saw, which is faster, safer, lighter, and less expensive than a large knife.
You can baton chips out of a larger log, making beaver-like notches in the wood. Again, the breakage occurs when you try to pry a big chip out. I think it is better to start a notch and break the stick off. If you can get a split started, you can use a rock or another stick as wedges to complete the split in larger stuff.