Adding a datapoint (or at least an anecdote):
We were recently writing a math library for a small embedded-like target, and started writing it in C. About halfway through the project, we switched some of the files to C++, largely in order to use templates for some of the functions where we'd otherwise be writing many nearly-identical pieces of code (or else embedding 40-line functions in preprocessor macros).
At the point where we started switching over, we had a very careful look at the generated assembly code (using GCC) on a number of the functions, and confirmed that it was in fact essentially identical whether the file was compiled as C or C++ -- where by "essentially identical" I mean the differences were in things like symbol names and the stuff at the beginning and end of the assembly file; the actual instructions in the middle of the functions were exactly identical.
Sorry that I don't have a more solid answer.
Edit to add, 2013-03-24: Recently I came across an article where Rusty Russell compared performance on GCC compiled with a C compiler and compiled with a C++ compiler, in response to the recent switch to compiling GCC as C++: http://rusty.ozlabs.org/?p=330. The conclusions are interesting: The version compiled with a C++ compiler was very slightly slower; the difference was about 0.3%. However, that was entirely explained by load time differences caused by larger debug info; when he stripped the binaries and removed the debug info, the differences were less than 0.1% -- i.e., essentially indistinguishable from measurement noise.