Though a new bike, or new bling on your existing bike might not make you faster in itself, if it makes you excited and happy and gets you riding more, then you will be faster pretty soon. So yeah, I'm in the "go for it!" camp

Depending on what you like/don't like about your current bike, new wheels are a great option. You can get some *really* nice and lightweight wheels for under $1,000 and they can liven up the feel of your bike a lot. Again, they may not necessarily make you much faster (though aero wheels can really speed up your descending), but just make it more fun to zip around on your bike.

On the other hand, a new bike is never a bad idea either