interesting idea !
it might but I don't know what sort of result you will get. if I were you ,(and if already you got the dish ready and neatly painted in white ,I'd give it a go and see the results but if doesn't work then you may consider buying an umbrella as they are fairly cheap especially on ebay ,which I think will do the trick.
do let us know if you try the dish,I 'd like to hear results of experiment
good luck