Data joined Starfleet in 2344, the same year as the Narendra III incident. The timeline shouldn't have been altered enough to prevent Data's joining, assuming it happened earlier in the year...
Or even if it happened later. It's not as if everything would've completely changed the moment Narendra III happened. A lot of things would've continued to go on pretty much the same path for years afterward. After all, it's a very big galaxy. As I was just saying in another thread a little while ago, in a Federation of hundreds of worlds, a conflict could have a devastating effect on the worlds directly involved yet have no impact at all on more distant worlds within the Federation -- much like, say, the disaster of Hurricane Sandy on the East Coast of the US had no direct impact on my life here in the Midwest, except insofar as I was concerned for friends and family who lived in the affected regions.
So a war would have to become really, really huge, on the scope of the Dominion War, in order to affect the entire Federation. It would've probably taken years for the UFP/Klingon conflict in the YE timeline to expand to that degree. So it's plausible that a lot of events would've been unchanged by the altered history for quite some time.