No, only if you increase the amperage of the circuit breaker. Doubling the voltage just doubles the power you can deliver over the same wire. To keep it the same, you can actually use a thinner wire. That's part of the reason long-distance transmission lines are at many thousands of volts.

You run two hots instead of one, that's 200% "thicker". Between the two hots you now have 240V. Between each hot and the neutral you have 120V like before.