If the bowl is not sturdy, then yes. You should buy a bowl that attaches to the cage or one of the ceramic dog bowls. You can usually get those from a Dollar General or any place that sells dog bowl. Just make sure it is heavy enough that he cannot dump it, but it doesn't have to be huge.
I have stainless steel bird bowls that attach to the cage. I got them at Petco. Plus they come right out of the holder so they are easy to clean.