More or less, yeah.
Though that's what kicked off our conversation in the first place:
Also, it's more helpful to think less about characters and more about works. You can't copyright a character like Sonichu, you copyright each work (like each issue of Sonichu) that Sonichu appeared in. If your work incorporates material from an existing work, the copyright holder can demand royalties or forbid you from publishing your work. But you still have copyright on what you created, even if it incorporates existing material.
This is important because people think that just because Sonichu rips off a bunch of stuff, that Chris doesn't own his own stupid scribbles. He definitely does own his scribbles. So if Chris got pissy at someone, he can demand they take down their fan art of Sonichu. Whether or not Chris can profit off of Sonichu himself is mostly irrelevant. (It factors in if Chris wanted to demand damages, but if he doesn't, he might still be able to at least get the fan art taken down.)
Of course, there's parody and other exceptions that might come up, both in Chris' favor and against.
And then there's trademarks, which are much more complicated.