In my opinion, ideally, to be a more well-rounded professional, it would be nice to know at least one programming language for the most popular programming paradigms (procedural, object-oriented, functional). Certainly, I consider R and Python as the two most popular programming languages and environments for data science and, therefore, primary data science tools.
Julia is impressive in certain aspects, but it tries to catch up with those two and establish itself as a major data science tool. However, I don't see this happening any time soon, simply due to R/Python's popularity, very large communities as well as enormous ecosystems of existing and newly developed packages/libraries, covering an very wide range of domains / fields of study.
Having said that, many packages and libraries, focused on data science, ML and AI areas, are implemented and/or provide APIs in languages other than R or Python (for the proof, see this curated list and this curated list, both of which are excellent and give a solid perspective about the variety in the field). This is especially true for performance-oriented or specialized software. For that software, I've seen projects with implementation and/or APIs mostly in Java, C and C++ (Java is especially popular in the big data segment of data science - due to its closeness to Hadoop and its ecosystem - and in the NLP segment), but other options are available, albeit to a much more limited, domain-based, extent. Neither of these languages is a waste of time, however you have to prioritize mastering any or all of them with your current work situation, projects and interests. So, to answer your question about viability of C/C++ (and Java), I would say that they are all viable, however not as primary data science tools, but as secondary ones.
Answering your questions on 1) C as a potential data science tool and 2) its efficiency, I would say that: 1) while it's possible to use C for data science, I would recommend against doing it, because you'd have a very hard time finding corresponding libraries or, even more so, trying to implement corresponding algorithms by yourself; 2) you shouldn't worry about efficiency, as many performance-critical segments of code are implemented in low-level languages like C, plus, there are options to interface popular data science languages with, say, C (for example, Rcpp
package for integration R with C/C++: http://dirk.eddelbuettel.com/code/rcpp.html). This is in addition to simpler, but often rather effective, approaches to performance, such as consistent use of vectorization in R as well as using various parallel programming frameworks, packages and libraries. For R ecosystem examples, see CRAN Task View "High-Performance and Parallel Computing with R".
Speaking about data science, I think that it makes quite a lot of sense to mention the importance of reproducible research approach as well as the availability of various tools, supporting this concept (for more details, please see my relevant answermy relevant answer). I hope that my answer is helpful.