Well, the only registers I had when Cygwin was installed were the ones in
HKLM\SOFTWARE\Cygwin\
and
HKCU\Software\Cygwin
the HKCU Cygwin key had two keys called Program Options and Setup which were empty (they only contained the (Default) REG_SZ which was empty)
The HKLM Cygwin key had the following sub-keys:
Installations - which contained some registers regarding an .exe C program I ran with cmd which had cygwin1.dll copied there and also, the install path of Cygwin.
Program options - which was empty
setup - which had a registry called rootdir with the install path of Cygwin as its value.
Anything else related to cygwin was what I added (the mounts v2 key) or the PATH variable.
Therefore, I think that C::B should add the registry key automatically if it doesn't exist, since, at least by default the registry that has to be added has a known name and value (cygdrive prefix and /cygdrive).
You can add a setting that is enabled by default to create that registry.
Or, you can add the compiler presets for cygwin by default. Just ask the user for the install dir.