I had that notification turned on for a while but decided to turn it off. If you get a lot of tweets, that notification will seem like a permanent fixture on the banner.
UberTwitter.
If you want the Native Twitter for Blackberry application, I would wait until its officially released. RIM might still be tweaking some stuff.
So far Twitter for BlackBerry is a great app, and to think it is still only in Beta phase. Uber is right up there as well and if I had to rank them it would be 1a & 1b because they are both AWESOME. TweetGenius is sweet for the graphics but with RIM'S app and Uber, why pay for something if you don't have to?
Ubertwitter is probably the best twitter app right now. Really lightweight, but it still has a lot of options. And with the rumors that push is coming to UberTwitter, there's no reason to get another twitter app.