Most people seem to prefer dry-enough-to-burn-easily wood but there are clearly exceptions, especially for peach which some people love fresh cut.
If you have some kind of smoking suitable wood available I don't think anything bad is going to happen if you start using it now, but personally I'd generally treat it more like firewood and set plenty aside for the future and let it do its thing.
Note that woods people smoke aren't what I would think of sappy or full of resin, like say pine. It's primarily a moisture issue and if you expect your wood to burn clean or smolder.