Yes, but not by a lot in most cases.
While the exact figures of voltage and current will vary wildly from device to device, increasing the volume of a speaker increases the amount of voltage sent to the speaker to make it create louder sounds. With this slight increase in voltage, you also get a slight increase in current, which will draw ever so slightly more energy from the battery. With something like a cellphone, the difference in current draw between a low speaker volume and a high speaker volume will be minuscule when compared to other parts of the cellphone like the cellular/WiFi connection, screen brightness, and the processor. On something like a giant portable guitar amp, the difference in current draw between low volume and high volume will be much greater and will have a bigger effect on battery life.
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