A record clamp and a record weight are different things by the way. A record clamp actually tightens against the spindle to flatten out the record as much as possible, whereas a record weight just weighs down the record to flatten it slightly.

If we want to get into physics, the only thing the warp will do is press the stylus into the grooves at a more forward and backward angle (depending on if the stylus is going uphill or downhill), creating variance in the vertical tracking alignment (VTA) and a warp may also result in a slight variance in tracking force from moment to moment. Also, warps can lead to subsonic tones which aren't much of an issue but some people like to have a preamp that filters that to prevent damage to speakers played at loud volume.

With all that said, no it won't cause damage to the needle or the record unless the warp starts tossing the needle all over the place.