yes of course, the recoil will be greater than the KE of the bullet; amazing grace. anyway, if the impact is inelastic, or at any rate if the bullet is totally embedded into the wood, all of its KE will be imparted to the wood+bullet "system" -- no matter how fast the bullet is going, contrary to what you seem to believe -- minus the amount lost to heat, although that is arguably also kinetic energy of constituent atoms.
it's going to be so easy for you to prove that KE is mvv, once you decide to look into it.
you hsven't proven anything to me, nor even given any kind of dimensional analysis of your strange formula -- I doubt that it even comes-out to "Galilean ubits" of mv.
