Just thought I add some info. Why I think the overlay isn't working when linking the launcher/bat is cause the process of launching a exe through a bat file is different from launching one within a exe and steam was designed to follow the exe's method so it breaks.
I've seen games with launchers that have the overlays in the game so it isn't a issue of steam launching a exe which launches another exe.
If that is the problem then the fix could be as simple as removing the bat file and having the launcher start the exe directly and have any dynamic args be pulled from the server at start or store them in some file where the launcher reads from. Or like remove the need for args and hardcode the values into the exe, but I think they are doing that to save patch size and/or to easily support events with local servers.
Or if I'm totally wrong and it requires actual steam api integration then ...
As far as I know, steam only monitors the single process and it's children, otherwise, the batch file would work. One method to work around the issue is to simply change the bat to exe and that should work (have not tested, AMMV). The problem is you would have to do this with every update. (re-run the tool to convert the batch to executable -- assuming that process even works)
If you do try that method (batch to exe) please let us know what software you used to convert, and if it was successful.
I just realized ... someone could just code a program to read the bat file's args and launch the game lol