Yes / no. An LPDA isn't a Yagi-Uda because all of the elements are electrically connected. So although the shorter elements behave a little like directors and the longer elements a little like reflectors, they also contribute directly to the current flow.Isn't a log-periodic array already desined to do this sans motors and gears?
The advantage of an LPDA is it provides reasonably consistent performance across a large bandwidth. However, a Yagi-Uda of the same boom length will provide higher gain using fewer elements but a narrow bandwidth.
So an adjustable Yagi-Uda should provide higher gain than a comparable LPDA.