No, you should learn one or more assembly languages and read some arch reference manuals and their supporting glue chip reference manuals if you want to learn "

No, you should learn one or more assembly languages and read some arch reference manuals and their supporting glue chip reference manuals if you want to learn "how the computer works" from the perspective of programming after reading an academic book or two on the subject of computer architecture. C is useful for participating in commercial application of these things, but it is possible to be a very accomplished C developer and have no idea how hardware interfacing works and I'd wager this category vastly outnumbers those that understand hardware interfacing.