Why modern warships can still carry figureheads

Can a modern warship carry a traditional wooden figurehead without disrupting its radar?

Yes. A modest figurehead placed away from the sensor arrays should have little practical effect on radar performance.

A modern figurehead is a decorative fitting rather than a return to the large carved structures of the sailing era. Its position and modest size keep it away from the ship's radar arrays and other sensitive equipment. The fitting can therefore preserve a visual tradition without imposing a meaningful combat-system penalty. This makes the question one of placement and proportion rather than a general prohibition on ornament.