It takes less than that. If you want to escape Mercury, you'd need to go Mercury's escape velocity parallel to the orbit, or greater if headed away from the sun, and less if headed towards the sun. So to burn up in the sun would be less than the stated or free-body calculated Mercury escape velocity. Also, the number is reduced because the calculated number is related to from a rest at the surface, not for something already moving in orbit. It wouldn't take nearly that much more velocity to end up orbiting the sun, or smashing into it, if you were already moving and in orbit.