Yes you can root a twig which does not have any buds left on it. However, only roots will form on the twig and it cannot develop into a tree. You need at least one viable bud left on the twig.

It is not necessary to "wound" a cutting before placing it in the rooting medium. When the cutting was taken, the bottom cut should have been made about 1/2 inch below the bottom node. Keeping too much wood below the bottom node sometimes delays the formation of roots. A nice clean cut allows for better formation of a callous and also helps keep out organisms that cause mold.

Not that you would ever want to DO it, but as long as you don't damage the latent bud in what would have been the future leaf axil when you remove all the buds from a cutting, it's possible to root a cutting with all conspicuous buds removed. As long as the cutting was taken from parent stock sufficiently healthy to endow the cutting with enough energy to activate the latent bud, there shouldn't be any reason it wouldn't root and produce a shoot or shoots.

Al