I feel very strongly about this. The fact that C++ is C is meaningless (although it is true). When you go into ANY C++ class there will be assumptions about how much C you know. Please read my example above regarding building a linked list class. And it isn't like the C++ class is going to spend time teaching everyone about C basics like pointers, arrays, and the like.
If you talk to the professor and he specifically says that he will teach C++ beginning with the assumption that the students have zero C knowledge, then possibly I'll relent. But, even then, you will learn more if you know C going in.
Again, the fact that C++ is based on C is meaningless in this context. The C++ constructs are built on top of (out of) C, and you should understand basic C going in. You use a lot of basic C in any C++ program.