Yes, wood is wood. However, if you've got a stave that you've dried yourself (air dried) the moisture content will be somewhere around 12% (up to 20%). If you then go out and buy a board (about 6% moisture content) and place them both in your shop (side by side) and then try to heat treat them, the board will burn first. OK, everyone knows that.
The tricky part is getting a stave down to 6% moisture content. If you can do it (with a hotbox or kiln) then yes, we are comparing apples to apples. Even so, I think the properties of kiln dried lumber and home-dried staves are different. I think kiln dried lumber resists the absorption of water and home-dried staves resist the release of water. Just my humble opinion.