Coming from someone who started strictly online, Offline made me 100x the player I used to be.
My scene isn't very strong or anything. However, just having older players teach you basics and fundamentals will make you so much better. If someone is better than you at the game, that will make you way better (especially if you become a challenge to them and they in turn start to step it up).
The majority of online players are bad. They don't adapt, they complain when they lose, and they don't try to step it up. Online is a good practicing tool, however.
Take it like this: I'm not good at all at Killer Instinct, however online I've lost MAYBE 20/100 fights. I suck at that game. Playing only good people online can make you a lot better, but even when I was doing that I still paled in comparison to most offline players in my scene once I started to come around.
But yeah, this exact scenario pretty much happened to me and made me a way, way better player.