No, the DirectX version behaves differently / the overlay gets differently injected.
I can only open the overlay in a DirectX project, when launching the corresponding app from the Steam-Library.
Within a DesktopGL project the overlay is even working in a quick debugging session.
You can test this in a fast way by adding your application as a “Non-Steam-Game” to your library.
There is a high chance that this is working for you. If it’s not, then you need to take a closer look at the support site, which I have posted above.