Good morning. Yes you can fit your recipe for (3) 9, inch X 2,inch round cake pan batter into a 13 X 18,X 2, inch pan. You must understand each pan manu sizes their pans slightly different as well as the radius in the corners as well. Bottom line assume 2/3rds full allowing for chemical leaveners you may just have enough left over for a muffin or 2.
One more thing, the chemical leaveners will not necessarily be required in exact proportion when the configuration of the baking pan is changed. I am not certainn if you employ slightly less or perhaps slightly more. Our member Julie can tell you more about this than I can as i do not bake large sized quanties.
Good luck & enjoy the day.