Like most people here, D2 isn't my first choice for cooking knives, but that said, I have been very pleased indeed with the few I've made, and the D2 outdoor knives I've made, heat treating by the method Nathan posted a while back.
A fine edge on one of these will do all the usual paper cutting tests just fine, and these would go beyond that and free cut in a spiral pattern in newsprint....that's a nice edge. Lasts very well, too.
The usual HT processes give you the crude, sturdy edge that you'd expect from D2. Probably great for most cooks.