It would affect how much time is spent, yes. Searching rubble and searching buildings are not combined into single actions - searching both a building and the rubble outside of it takes two actions, whereas searching only the building or only the rubble takes one.

If Zelda waits for Lea, they will be moving at Lea's pace - meaning that although Zelda hasn't spent as many actions as him, there will not be enough time in the day for her to continue all the way on.