Can a plate with incompletely filled LB agar be used?
It won't be a problem other than that the surface would be uneven. Seal the plate with parafilm when not using to avoid moisture from accumulating inside. When you pour plates then swirl the plate gently so that the molten agar distributes evenly throughout the plate. The agar will be thin though, and you would have to streak gently so as not to cut the agar; you can add 0.5 % of normal agar-agar to make it a little dense. 

Or else use  smaller plates (2 inch) if you have them in your lab.