create a static block under CMS in admin and name it something like category_product_banner and either upload your banner image or add the image code in the editor. Click save.
Then go to admin CMS widgets and create a new widget type = static block Design Package/Theme = your theme.
Widget Instance Title = category product banner
Sort Order = whatever you choose or leave blank.
Then while your on the same page scroll down and view Layout Updates.
click add layout update
pick your chosen destination Page: Block Reference: Template:
I am not sure if you can get the banner to display exactly where you wanted it but you will be able to get it on there. You might need to change the banner size and add it to a column, footer, header.
If you add images to core files they will not be visible if you upgrade your version.
Oh ya make sure and select block type to reflect the static block you created category_product_banner
Hope the best for you.