In a double planet, the radial velocity wouldn't appear too different, at least no more different than a planet with a giant moon. Differentiating between double planets is similar to attempting to detect extrasolar moons, which has not been done. I would tentatively say the only way to detect it is via high-resolution direct imaging, or transit light curve.
Stepping out of the bounds of what might be realistic, I'm guessing close double planets produce gravity waves that would propagate through the system. Perhaps this is sufficient to slightly modify the orbits of other planets in the system. Perhaps this might be detected with radial velocity.
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