No.
C is going to be around and useful long after COBOL is collecting dust. Too many core things are built with C. The Linux kernel, the CPython interpreter, etc. Making C go away will require major rewrites of projects that have millions upon millions of hours of development.
Even Fortran has a huge installed base (compared to COBOL) and is still actively used for development. Sometimes the right tool for a job is an old tool, because it is so well refined for a specific task.
Forth anyone?
The rewrite-it-in-rust gang arrives in 3, 2 ...