Also, even a mediocre C# (programmer) will be able to produce a working program faster than a good C++ programmer!
I feel like that difference shrinks as the caliber of the programmer goes up. Will a really good C++ and C# programmer be appreciably faster when working in C#? Not sure. C++11/14 with extensive use of standard libraries (and good 3rd party libraries) can be very expressive, and also pretty safe if you choose to use a safe coding style (which may or may not come at a performance cost). Certainly it's faster to write some things in C++ compared to e.g. Java, even for a klutz like me.
At the low end of skills the difference is the most striking. I think it's accurate to say that a poor C++ programmer will generate negative value to a project. With C++, either plan to get pretty good, or spend your time more constructively with another language.
If you mean faster as in programmer productivity, then yes, a really good C++ and C# programmer will be faster in C#, often by an order of magnitude. That's a side effect of the purpose behind each language. The design principals behind C++ of pay for what you use and that undefined behavior should be decided by the programmer has a cost on productivity.C# doesn't follow this ethos at least not as closely. As a result things like runtime type information is just much more accessible in C# and more pervasive in the libraries.
Oh, and of course that is the biggest productivity win of C#. As languages, C# and C++ aren't really all that different. Some aspects of C# are much cleaner due to the newness of the language ( generics for example ), but at the end of the day this isn't the stuff that profoundly effects productivity. (Although spend a weekend working with LINQ and you will have a hell of a time going back!) Nor really is memory management, the normal big boogieman. No, the big difference is the standard libraries. C++ has improved quite a bit since STL then Boost, but compared to C#, they are absolutely shit. Sit a great C++ programmer down beside a great C# programmer and ask them to accomplish many common programming tasks... read an XML file, string manipulation, parse and transform data, make a network connection, archive and expand a file, etc... and the C# programmer will generally spank the C++ programmer. There are exceptions and edge cases, but they are just that.
Then of course are all the other little things that add up as performance wins. The compile/link cycle for example. The lack of cruft is another big win in C# ( and to a much lesser degree Java ). These things all contribute to programmer productivity.