Pretty much, two things here.
1) Online does count. It just has lag that can screw things up. But that doesn't mean all player skill goes out the window. And what THAT means, is that no, you don't get to just claim "online doesn't count" to make excuses for when you lose. Because hey, guess what, misreads happen offline, too. Only when a match is unbearably laggy to the point where you can't even move, does it not count. But you don't get to just call mulligan because of a misread here and there, or because the framerate is lower. If you can't compensate for variables, thats on you, it doesn't mean the game sucks. And since half the point of DOA is that constant "X Factor", if you can't account for that, then you probably shouldn't be trying to play DOA, online, or offline.
2) Online community is generally better than offline, since the "ragers" are unique to the FGC in that they are present in both offline AND online. I mean, you can just look through this site (or this thread) and see that a lot of the "offline" players are elitist, and that turns a lot of people off from caring to try local tourneys and stuff. You get more "regular people" online, who are generally a LOT friendlier than the standard tourneygoer.
Aka, yes, online can be laggy. But "lag" doesn't mean "unplayable." Lag can range anywhere from minor framerate to completely unplayable. But unless its UNPLAYABLE, you don't get to just call mulligan and say online doesn't count, and player skill online means nothing. Just because you can't do your standard combos doesn't mean the game sucks, it means you do, switch tactics and adapt. If one thing doesn't work, try another. Its only when NOTHING works, that it goes into "doesn't count" territory. And "missed the timing" doesn't fall into "doesn't count" territory.
Online counts, AND offline counts. The only time online doesn't count is when it is so laggy the framerate is borderline zero, and when you press a button, nothing happens. Like I said, actually unplayable. And if that comes up, its on YOU and the opponent, that's your internet connection, do your part and fix it so you can play online normally with everybody else.