Cavalary: Oh. That's rather too much hassle for it. And if there are .bin files, as long as the .exe opens, it should be fine, so this would only be relevant for smaller games, where the entire installer is the one file. Still, you'd think they'd make it somewhat easier. Or that the .exe would also check itself and have the checksum inside as it does for the .bins...
I'm afraid it doesn't quite work that way.
I'll start with the last first.
Once you create the EXE (installer file), then you get an MD5 for it. If you then embed the MD5 value, you have in fact altered the EXE file, so the MD5 value is no longer applicable. There is just no way around that, except providing the MD5 value externally.
When you open or run the EXE file, it may or may not check any associated (companion) BIN files at that point. When you start installing though, and it extracts each file, it may then do MD5 checking of each file as it is extracted.
As many would know, some GOG games take an age to install, certainly the large ones. No doubt that is why.
EDIT I recommend having a try with InnoExtract in Test mode, and you will see what is being revealed in the console.
A simple way to do that, is with my
GOGPlus Download Checker program.
https://www.gog.com/forum/general/gogplus_download_checker