If you could get isotopically pure Pu-239, which doesn't exist, it would work - but even the tiniest traces of Pu-240 will spoil it. Quoth Wiki: "The presence of the isotope plutonium-240 in a sample limits its nuclear bomb potential, as plutonium-240 has a relatively high spontaneous fission rate (~440 fissions per second per gram—over 1,000 neutrons per second per gram), raising the background neutron levels and thus increasing the risk of predetonation."
Long story short, all those extra neutrons make a chain reaction far more likely to occur - so likely that if you use gun assembly, supercriticality is reached long before the two pieces are physically together and they just blow back apart with a negligible yield. Granted, "negligible" in the sense of nuclear weapons means anywhere from a few to a few hundred tons, and there's still an intense load of radiation and fallout, so for terroristic purposes it might suffice...but you aren't building a city-leveling device with Pu and a surplus artillery barrel.
Anyway, breeding it with a neutron tube would be slow, Like building a skyscraper with a set of Craftsmen tools slow. Reactors are the *only* way to synthesize >mg quantities of any transuranic. If you have those resources, a simple (albeit large) implosion system is pretty much trivial.