No, it won't give you more power or speed on the highway.
An overdrive is simply an additional gear that reduces the engine's rpm while cruising on the highway. You use less gas. It also reduces the torque transmitted to the wheels so I believe it's recommended that it only be turned off when under heavy loads, like towing.
Turning OD on and off would be like comparing an old 4 speed manual, where the 4th gear ratio is 1:1, to a 5 speed where 4th is still 1:1 but 5th is 0.75:1. Traditionally, OD does nothing to the behavior of the other gears. In a modern, electronically controlled transmission however, OD may also do some other things like adjusting the shift logic, maybe.