You want a tube amp with a low output impedance. Typically, one with output transformers because tubes have a high output impedance. The only OTL with a low output impedance is the Zana Deux, because the 6C33C has a low output impedance.
If you use an amp with an output impedance higher than the headphone impedance, you lose the damping factor and control is poor.
Yes, it will "work," but your headphones won't sound anywhere as good as they could.
Solid state always has a low output impedance. It's always cheaper to buy a quality solid state amp than a quality tube amp with output transformers. The output transformers and high voltage power transformers are expensive. Probably $300-$400 for quality ones, not counting everything else. Solid state also costs less to manufacture (generally), so solid state is the best option on a budget.