A cult? Yeah, right. Just like Zoro and Nami and Luffy and almost all the Strawhats tend to "leave things to Luck". So they are also a cult, aren't they? :p And besides: The only one who really mentions luck all the time is that ill one, if I recall correctly. That's probably his quirk, just like Zoro is sleeping all the time.
But back to the topic: Luffy showed real ambition because he didn't fight against someone who isn't worth it. Blackbeard himself said: "If you want to be a first-rate man, you'll encounter a time when there's no reason to fight back". That's what impressed Blackbeard, and not some weird kind of fighting spirit that makes people crumble.
And later he clearly refers back to Luffy's first encounter with Bellamy, because that's the only time he met Luffy: When Luffy showed that he has too much ambition and too many more important things to do than to waste his time on some minor enemies.
It is possible that Luffy will get some kind of fighting spirit that makes people crumble. Just like some kind of extreme determination and killing intent which people subconsciously sense and that is strong enough to make their willpower shatter.
But I see absolutely no connection whatsoever to what Blackbeard said besides the fact that Luffy has the ambition to aim to the top. But we know since the very first Chapter of One Piece that he wants to be pirate king, so that knowledge isn't something that surprise us at all.