Does it though? Its without a doubt successfully but I was under the impression that PJ never quite left the sphere of teenage novels. It hardly has the power of Harry Potter and its subject matter being Greek myths ensures it never will. Besides I always thought the similarities with Harry Potter was more of a weakness than a strength.
When I say "Percy Jackson" I'm referring to the wider "Riordanverse" as well, so that includes stuff like Carter Kane (Egyptian gods), Magnus Chase (Norse gods), and everything else (the Rick Riordan Presents series has other authors delve into various pantheons; Hindu, Mayan, Amerindian, etc.) But that wasn't the point of your question.
From where I'm standing, the short answer is no. I don't think Percy Jackson will ever be as popular as Harry Potter. That said however, while I do only have anecdotes, they do paint a picture. So here's some tidbits:
-On ff.net, the Harry Potter entry is the largest books entry and the largest ones on the site, at 821,000 entries. Percy Jackson by itself has 77,500 entries. Compared to Harry Potter, that's small fries. Compared to all books though? That's the third largest. And I'm not counting the other Riordanverse entries there. It's debtable how representative fanfiction is of how popular a work is, but it's something.
-In the realm of personal anecdotes, library work does give me insight into what "kids these days" are reading. And the Percy Jackson books are definitely among them. In the realm of junior fiction to YA, I'd say Percy Jackson is the most popular, at least by number. I don't know if it's more popular than Harry Potter per se, but it's up there. Again, not the best test, because there's more Jackson books than Potter books, so I'm of course going to see them more, but the Percy Jackson series clearly has an appeal that spans the JF/YA ladder, in the same way that HP does.
-In recent times, I've seen a push for Percy Jackson to be an "alternative" to Harry Potter. Again, this is all anecdotal, but it keeps coming up. Type in something like "Percy Jackson vs. Harry Potter," and once you avoid the Death Battle links, you'll find essays arguing that the Percy Jackson books are better, and having read/watched some of them, the points aren't without merit (like this isn't some kid yelling, it's a reasonable argument, at least on the surface). And it seems that Rowling's "transphobia" has had people holding up the Jackson books as a "progressive alternative" or something. Like, saw an article citing how a parent will now refuse to buy Harry Potter books for their child, and will instead buy them Percy Jackson books. Or another how Riordan understands representation better because he has a Muslim Valkyrie or something. I can't help but roll my eyes at a lot of this, but the push is there.
And it's notable in another sense. I was 8 when the first Harry Potter book came out. I was there when the series came out, and when it really exploded in popularity (round about Prisoner of Azkaban). Again, this is simply first-hand accounts, but Harry Potter wasn't the only children's series that got big around the time. Artemis Fowl and A Series of Unfortunate Events also tapped into the zeitgeist, at least at the school I went to. But Harry Potter remained in the zeitgeist, while those two didn't, or at least, not to any comparable extent. Percy Jackson, right now, might not be as popular as Harry Potter, but it does appear more popular among its age groups than those other series ever were. Like, I dunno, maybe Harry Potter is Nintendo, and Percy Jackson is Sega, and decades from now we'll have
Book Wars: Harry Potter, Percy Jackson, and the Battle That Defined a Generation.
TL, DR, Percy Jackson's more popular than a lot of people realize.