Not in my experience. Currently my man open source project consists of some 70,000 of C which compiles as C++. Maintaining C++ compatibility takes very little effort. I tend to switch to C++ before a release, to catch regressions. Often there is nothing. The most I spend is maybe five to ten minutes fixing some minor things. Some of those minor things have nothing to do with C versus C++ like signed/unsigned warnings.
Note that these signed/unsigned warnings from GNU C++ actually found a real problem: I had code which assumed WEOF was negative. (It was originally char based code that was switched to wchar_t; of course EOF constant in the narrow character world is negative.) The GNU C++ compiler also identified the situation in the same code that a variable that should have been wint_t was mistakenly int.