If you are having trouble getting Diablo 3 to work with the Steam overlay, the trick is to force it to bypass the launcher.
For some reason, on some computers, the steam overlay kind of tags itself to the launcher and goes away when the launcher goes away… To fix this, make sure you are launching from Diablo III.exe.
Right Click on the shortcut in your steam library, go to properties, and first look at the target location. It should be something like “C:\Wherever You Installed the Game\Diablo III\Diablo III.exe”
If it says Diablo III Launcher.exe, remove the launcher part.
Finally, add to the end of the location “-launch” without the quotation marks and on the outside of the quotes in the properties menu.
If it’s right, it should look like this:
“C:\Wherever You Installed the Game\Diablo III\Diablo III.exe” -launch
If this is what you’re seeing, it should work.
Note that you won’t be able to access the launcher this way, however, if a patch is released, Diablo III should kick you out to download the patch or something. If it won’t run because you require a new patch, just open Diablo III outside of steam to resolve this.
I hope I’ve helped someone.