That depends on what you define as a "C program" and what you define as a "C++ program".
All C code will compile and run with C++ compilers, because C code is a subset of C++ code, but some purists would say that even though the code compiles and runs, it doesn't constitute a C++ program because it's not using, for instance, C++ input and output. C uses functions such as scanf(), gets() and printf(), while C++ uses stream classes and the << and >> operators.
But I'm more liberal and would answer your question with a "Yes".
Hope that helps.