In terms of what the language allows you to do, yes. However, if you're a C programmer, you can pretty much just keep writing the same code you've always written (minus the preprocessor, thankfully). You can even compile C code with the D compiler and call those functions from your D code without doing anything further. That's definitely not the case with C++.
D is D.
You only need to compare how C++ and D treat a class type, and you know straight away they are miles apart (I prefer C++ in this regard).
D has a subset, and that subset is more like C - pretty much cause that subset is C. That can be interesting to use, since it's like C with modules.
But don't be fooled. D is not like C++.
I wish people would stop saying as such, cause it's not at all true.
As for classes, just pretend you are using structs in C++, and use structs in D.