I'm not sure what you mean by "DB Pro Free" (do you mean the version available on GitHub? which is v7.2 but can easily be updated to v7.7)
There should be no issues changing the Application Icon via the method Bored showed... in-fact the App I built for the Mario Sunshine Water Shader (in the AppGameKit Classic Forum) which is a DBP app, is using a custom icon.
It was built with the "Free" version of DBP from GitHub.
Have you considered the issue is with the .ico you're using... specifically it has to be a Windows 9x Compatible Icon.
I've added the Photoshop 64bit Icon Import / Exporter Plug-In as an attachment that's compatible with DBP.
I don't have the 32bit version, and can't remember exactly where it's from but it supports Creative Cloud versions of Photoshop (including 2020)
Just be sure to keep the ICO smaller than 48x48, and I'd recommend 8bit Indexed Colour with a Transparency Key.