basic 3-phase transformer question

Could you tell us what the primary and secondary vectors (connections) are for this transformer?

Steve Lockridge Alfa Transformer

| If the secondary has a load on 2 phases but nothing on the third, | Will one phase of the primary draw nothing?

That depends on the transformer phase configuration. I would expect a WYE secondary for what you describe. But the primary could be WYE or DELTA. If the primary is also WYE, then the 2 corresponding phases of the primary will draw current, and the other will not. But if the primary is DELTA, two of the primary _windings_ will be drawing current with the phase in common between them having more current and the other two phases having less.