I learned C before C++, and yeah it would be dumb to say that C++ would be easier if you didn't know C.
I don't mean that you can't learn C++ without C, but it's funny how people tend to act as if C was more of a handicap than nothing..
Both languages have the same origin, actually C++ is even like an extension of the C. Knowing one of them will be a huge help when it comes to learn the other. And it works both ways.
I think the big difference is C is a procedural language while C++ is an object oriented language. So if you know C++, you can definitely figure out your way around C, but probably not the other way around because you need to learn the object oriented mindset. I think another difference is that C++ has a string class while you have to build strings out of arrays of characters in C.
If the C++ course is for beginners and assumes you have no prior knowledge in programming, I don't think you'll learn much about classes and object oriented programming, so it'd be very similar to learning C. Its probably best to look up the differences and what the course teaches and decide for yourself.
Actually I would say the exact opposite. It works both ways, and especially from C to C++. People need to stop talking about OOP as if it was so much of a big deal. And that's even more true if he knows Java already. The best language to get to learn C++ is C. That's how I've been doing, and how look, I use C++ everyday, I love it, and I'm alive. OOP is just a mindset, as you said it. You'll get all the keys with the habit, which is given through the training, as for anything else.