Even with all the timeouts due to server overload, I was still able to play for a good amount of time already, and am level 7. I also saw people around level 8 and 9 while I was level 4, so I'm pretty sure that if you just be persistent about it, you will get to play it. Regardless, Rockstar is working on it, as they obviously want DAT VIRTUAL CASH MONEH from the pay2win mindset players.
I have been trying since the patch is out. Sure, I made a 1 hour break and tried out the BF4 beta, but it still doesn't work. And yes, I am disappointed. Did I expect problems? Yes, I did, it would be silly not to. But I can't even play the goddamn game, because R* apperantly doesn't have enough servers. From the sales they could have figured there were more than just a few people on day one of the Online launch. It's a fault on R*sides which could've been avoided or atleast be smaller, anyone who denies this needs to get his head out of R* ass.