Not by default (Maybe there is a way with a script). When you create an action for moving an object using the free transform tool, you're moving that object relative to the canvas and not another object. So if you record an action to be left 100px, the action with record that as a percentage.
What you could do
If you are creating artwork using columns. You could create actions that would move objects at varying length. So action 1) moves object 10% from the left. Action 2) moves 20% etc. However this would only be benificially with documents that use the same widths.
But this really isn't better than using guides and snap to guides.