binmode only changes the file handler from TEXT mode to BINARY mode. So that when you read/write a file, the file stream knows that it is Binary, and not Text.
Binary mode is necessary if you are reading/writing a file that is not text, such as an image. An image is binary, so you must use binmode to read it. Binmode can not be used to do or "make" anything.
In other words, you can not use binmode to overlay images. If you wrote your own image decoding algorithm to put the pixels together manually, you would need binmode to do that. This is what ImageMagick is meant to do for you. You do not want to rewrite something that complicated, especially if it has already been done for you.
Do not forget about the alternative of using
PerlMagick, it may be more stable than relying on the browser to work correctly with CSS.