No, not usually. In my experience anyway, most random engineers in the semiconductor industry that you would run into who know both C and Verilog would be just using those tools to do their job. There is a lot of ECE stuff to unpack in your question, but the subfield of ECE in question is called VLSI. You'd want to talk to someone who works in VLSI, or did VLSI as their focus in ECE undergrad or grad school.
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