Via the Debug C/C++ file button I see cl.exe and LLVM clang, but not mingw g++. I see it being added as a known compiler in the TypeScript debugger, but then something is causing it to not get used when it seems like it should be.
UPDATE: I didn't notice the logging logger.getOutputChannelLogger().appendLine(localize('debugger.path.not.exists', "Unable to find the {0} debugger. The debug configuration for {1} is ignored.", "${debuggerName}", compilerName)); -- maybe an "info/hint" entry could be added to the quick pick showing that g++ is potentially available if the user were to install the missing gdb.