I learned C after I learned assembly language. As a matter of fact, when I was reading the C programming language book, I would write sample programs, compile them (what was it, the -S option? Been so long) and look at the assembly language output to figure out what was going on. (The architecture I was doing this on was the Motorola 68000.)
Now, using a lot of C, people will probably get familiar with how pointers work, gain experience with malloc and free, and a bit of longjump would help also, even if they don't know assembler. But I think they'd catch on to the concepts a lot sooner if they had a dash of assembler to go with it. Particularly with experience writing a few interrupt service routines thrown in for good measure.
Also, they wouldn't go around showing off their ignorance by saying C is an 'advanced' or 'universal' assembly language.