So, the answer is yes to both possibilities. Android as an operating system is designed to use as many resources as it knows it has available to it. So, the GPU will be leveraged in a lot of places where it's appropriate. The app drawer is a good example, they use the GPU to render the icons as textures on a cube so you can swipe through from page to page smoothly. The Photobooth like video effects they showed off at Google I/O will use the GPU to render those effects live. And as more and more phones use modern GPUs, they will no doubt add more of these optimizations.
The GPU, however, can be used for even more and a lot of that is up to the device manufacturer. The best example of this comes from Samsung who leverages the GPU in their Galaxy S II and Galaxy Tab lines to create a smooth UI experience and even use it in their browser to smooth the scrolling experience. HTC has a tendency to utilize the GPU to add dazzle effects, window dressing on the Android tableau. Motorola does the same thing though not to the same degree. The result is that HTC's GPU use isn't as effective at creating a smoother UI, nor browsing experience, but shows off more animations and effects.
So, basically, you might never get an absolutely smooth browsing or UI experience because they'll generally add as many bells and whistles as they can, regardless of the performance. If you absolutely have to have the smoothest experience, get the Google Nexus. Samsung is their build partner and they are experts at eking out the most out of their devices. Either way, let us know what you get.
Jason