Absolutely.
There are three things that can have an effect on balance.
Engine rotating assy, converter and flex plate. (and harmonic balancer in the front) but we'll skip that assuming for now it is the right one.
If the engine (rotating assy) requires external balancing, it needs a balanced converter or a balanced flex plate.
Either one could have the balance weights.
He could have balance weights on both as well, which would also cause a vibration like you describe.
340's are internally balanced so if the converter and trans were from a 360 or 318 there's the problem.
