But if you know C#, C++ should be cake. The C languages are quite similar.
No. C# may borrow some C syntax (just as many other languages also do), but C++ is chock-full of oddities that make it infinitely more difficult than C# (or Java, which is very similar). Not only does it have countless features neither C# nor C possess, C++ has protracted (but useful) initially nonintuitive behavior that is oriented towards expert programmers. Add to that C's low-level memory management, which C++ inherits, and different runtime mechanism, and it's a whole different game.
Mastering the dangerous tools that are C/C++ . . . implies a competency in the general ability to deal with complex systems. . . . a competency also implies a competency with basic computer architecture.
This. Many, including myself, will also add that knowledge of an assembly language is a further demonstration of competence.
But it would help you, overall, to get your feet wet in C++. Try the google channel "programminghelp.org". It's where I learned, and he's quite descriptive.
Would it be worth it to make a simple game with C++ using an engine/library that's more similar to what I might be expected to use at a professional studio?
I'll be honest. Fewer new games are written in C++ than in any other language. This is partly because C++ is less preferred, but more because C++ is a difficult language to program right. A game you write in C++ will likely end up less featureful, more fragile, and less profitable than the same game if written in any scripting language.
That said, the exercise of (re)learning C++ is worthwhile (for all the above reasons), and a simple game is a perfect way to start. If it were me, in addition to writing in C++, I would try to do as much implementation as possible without a library. This is make your task still harder, and likely the end product still worse, but you'll learn much more. If I were hiring, implementing a simple graphics layer around OpenGL is far more respectable than calling callbacks through Ogre. Und so weiter.