What is the weight of a 4'x 8' 1/4" luan plyboard?
I plan to use a 6'x 2 1/2' sheet as a standalone cabinet door. What would be its tendency to warp over time?

I've done it, start with a flat sheet, use plenty of pocket hinges, and adjust them all the same, use the same finnish on all sides. If you want to be sure rout in angle iron the entire length ant use push style magnet catches top and bottom. Or just use a regular hollow / solid core door they come in luan and pivot hinges