I think that if you are going to teach someone the craft of programming (which is different from computer science) --
really teach them, you should follow what I call the Old School Curriculum. The Old School is based on the way many kids learned to program in the 80s, and the 80s version went: first BASIC, then assembly, then Pascal.
The first language you should learn should be a doddle to learn, even if it isn't very powerful. This was BASIC (or sometimes Logo) back in the 80s, but you could probably substitute Python or even Scheme today. This language teaches you concepts like these:
* Computers follow instructions supplied by the programmer
* The instructions have to be carefully worded in order for a computer to follow them (i.e., intro to errors and debugging)
* Arithmetic and mathematical operations a computer can perform
* Computers can remember things (i.e., variables)
* Computers can interact with the world (input and output)
* Computers can make decisions (conditionals and program flow control)
These are the very fundamentals of programming and it's amazing how many people haven't internalized these concepts at a deep level.
You can actually get very far with BASIC -- entire companies have been run with BASIC code. (Software written in and for Business BASIC variants was a major industry back in the 1970s and 1980s.) You can get even farther with Python. But once the learner is ready to go deeper, it's time to begin Phase 2.
The second language you learn should be assembly, which familiarizes the programmer with how a computer actually works at a fundamental level, as well as important concepts like CPU word length, memory addresses (essential for understanding pointers), program call and return (and stacks), etc. You don't have to even complete a large project written in assembly to get the benefits of this low-level, bit-twiddling learning.
Finally, the last language you learn should be Pascal. C or C++ would be today's equivalent. In this phase you synthesize the knowledge of high-level programming, structure, and control flow that you learned during your "BASIC" phase with your low-level understanding of machine details that you learned during your assembly phase. Then, the details of how and why the language works the way it does make much more sense.
So yes, to me it makes total sense to teach C -- as (at least) a third programming language, perhaps after several years of proficiency are acquired in the other two (depending on the student).