You probably don't need to learn C and program in it, but I do think knowing material covered in say [1] Computer Systems - A Programmer's Perspective will make you a better engineer, and historically computer systems were implemented in C and that heritage is still with us. So, being able to read C at least is a prerequisite to understand some of it.

[1] - https://www.amazon.com/Computer-Systems-Programmers-Perspect...