Sure you can be both. These labels aren't too important though. It's more of who you play.
Take UMK3 for example. Sure, I got my practice and experience through online play, but this doesn't matter. It's a matter of who I've played and trained with. I've played thousands of different players, all with either different or similar playing styles. So almost nothing can surprise me and I've seen everything you can do really. When we compare this to the offline players, some haven't seen everything or every tactic there is. This can be shown when we look at Summer Jam, no one knew how to handle IGB's tactic outside of a couple of players. This tactic is used frequently online, so a lot of online players would know how to react to it.
This is all about who you play against. Almost none of the offline players at SJ knew what was going on. And I think Joe had never seen that in his life, judging by what I heard. This is not to say "oh, online is better because of this", not at all. Just that it doesn't matter if it's online or offline, it matters who you're playing.
I played UMK3 for a whole year and was barely average. I played randoms all day and some friends who were equally as bad as me. It wasn't until I started playing better players did I see some improvement.
This may not answer your question, I just think it matters very little if you're an online player or an offline player. You don't learn
that much from this information. There could be an "online player" in Japan who plays Daigo everyday online. Never gone to a tournament in his life. After this training with Daigo, I would bet anything he would do very well at a tournament. At least if he played mostly Ryu's,