Interesting. You write, the overlay will not displayed. Maybe it is similar with the problem, that the app can even crash (and since the latest version of steam, it will definitely crash on actual wine versions). So you could try the following:
Solution: The compilation way
You simple "patch" the source code of the official open source imm32.dll of wine.
$ git clone git://source.winehq.org/git/wine.git ~/wine-git
$ cd ~/wine-git
Optional, but highly recommented:
$ nano Makefile
and change "prefix = ..." to "prefix = /tmp/wine".
do the same with "ac_default_prefix = ..." in the file "configure".
Now apply the patch:
$ nano dlls/imm32/imm.c
Search for this line: "BOOL WINAPI ImmProcessKey("...
and insert after the "TRACE("... line this new line:
Please to not forget the ";" char.
Thats all! Now compile:
$ make ./configure
$ make depend
$ make install
If you are using PlayOnLinux, you can simply add a new wine version:
$ cp -r /tmp/wine ~/.PlayOnLinux/wine/linux-x86/1.7.x-imm-patch
In PlayOnLinux, select the Steam entry and press on the configure button in the menu bar and select the wine version "1.7.x-imm-patch".
You can read it on my blog, too: