Yes, but not for the reasons Marxists think.

Should economists all be required to read, “work through”, and understand Adam Smith and Karl Marx? Is the discipline “fake” because most haven’t done this?

First of all, it’s important to point out that studying history of thought isn’t always useful. Just as doctors usually don’t study the works of Galen, and physicists usually don’t read Isaac Newton, economists don’t really have to read the original works of Alfred Marshall to understand supply and demand, or read John Nash’s original papers to understand game theory. The most useful concepts in science stand alone, divorced from the thought process of their originators. This is why they’re so powerful — anyone can just pick up Newton’s Laws or Nash Equilibrium and just use them to solve real-world problems, without knowing where those tools came from.