you'll need to take the needle out and have a look, it's usually pretty easy to see if the end is bent. The tip where the needle pokes through is hard to see, if you have good eyes, hold it up to the light until the light catches the rim of the hole (it is pretty small, you might need a magnifying glass), and rotate it, you should be able to see if there is a split in the tip by the way the light catches it.
If the base coat sprays without splatter, it is more likely to be an issue with the paint/pressure/thinning ratio. If it was a damaged tip or needle, I'm pretty sure it would be splattering no matter what paint you were spraying. I know mine was.
I find mine (Badger 150) spatters with paint that is too think and too low a pressure, since the paint is not atomising properly. I find paint that is too thin and at too high a pressure tends to atomise fine, but either comes out way too fast and causes runs (if I'm too close) or dries before it gets to the surface causing grittty finish.