Sure, keeping rigid arms may make a sprint more efficient, but it will also reduce the energy output because you aren't using your arms to help propel you. The bike rocks side-to-side during sprints to move the pedals relative to where the feet would be if they weren't moving. When properly timed, rocking the bike will move the downward-moving pedal up against the foot and the upward-moving pedal down against the opposite foot. Simply put, that means you are adding some force from your arms to the force already being produced by your legs.

If this is a problem, the long-term solution isn't to eliminate the rocking, but rather to get the timing right so that it adds to the pedal stroke. Watch the bikes of any group of professional pack sprinters accelerating at full throttle; they're certainly not staying upright, and their arms aren't rigid either.