If you pipe a random process into an image viewer, eventually you will get an image that can be compressed with PNG compression. If you let the random process run, you will eventually get enough of these images compressible by PNG that will allow you to save enough bytes to fit in a PNG decompression library. This may only occur after a ridiculous amount of bytes, but it is guaranteed to eventually occur following the properties of randomness.

So the method will work, but it may take a very large amount of data before it does. If the method does not work, it implies that a random process cannot generate an image that can be compressed with PNG - and that is definitely false.