It turns out that Mono DID turn off GC messages as the default. See this issue I posted on Github for details: https://github.com/dotnet/android/issues/6483

The resolution is to use the following adb command to reenable the log messages:

$ adb shell setprop debug.mono.log default,mono_log_level=info,mono_log_mask=gc

Note that this command needs to be sent before the application is started.

Note that you can also set these environment variables using an environment.txt file that is compiled with the application.