No...
By the usual understanding of terminology, I do not think that it can be a Dragon if White does not do the e4, Nf3, d4, and Nxd4 thing.
By the usual understanding of terminology, I do not think that it can be a Dragon if White does not do the Nf3, d4, Nxd4 thing. I am just guessing, but perhaps you are wondering if a Dragon book will completely prepare you to play the 1 e4 c5 position. That does not seem likely.
Looking in MCO15 (from over a decade ago), I see the Dragon given as 1 e4 c5 2 Nf3 d6 3 d4 cxd4 4 Nxd4 Nf6 5 Nc3 g6. About half a century ago, I think that one might see 1 e4 c5 2 Nf3 Nc6 3 d4 cxd4 4 Nxd4 Nf6 5 Nc3 d6 6 Be2 g6. These days, there are sometimes lines like 1 e4 c5 2 c3 g6 3 d4 cxd4 4 cxd4 d5 5 e5 that, I suppose, somebody might consider to be kinda Dragony, but my guess is that a book on the Dragon would not be of much help for Black in dealing with that last line.
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Can you get into the dragon no matter what white plays, or can they make moves that force you to place a different type of the Sicilian?