CSS already has a property for rounded corners, called border-radius.
This is supported by virtually all browsers in current use. The only exception of any significance is IE8 and earlier.
The good news in this case is that IE8 can indeed be programmed to work the way you're asking. Other browsers cannot, but IE can, and this is lucky, as it's the one browser that needs it more often than most.
So the direct answer to your question is "sometimes". Most browsers drop the styles they don't support, but IE keeps them. It obviously don't do anything with them, but you can access them via the DOM, which means that you can do what you're asking.... but only really in IE.
In the case of rounded corners, there is already an excellent Javascript-based hack for it called CSS3Pie. This is open source, so you can examine their source code to learn how it's done.
The CSS3Pie code is quite complex though, so if you want a simpler example to work from, take a look at this older script which does the same thing a lot more simplistically. Easier to read, but not as functional. For real life use, use CSS3Pie, but for learning, this one is a better starting point.
For working with IE, I would suggest following the examples in these scripts to achieve what you're asking. For other browsers, you will have a much harder time.
border-radius. Also, you might want to check out something like css3pie.com to save you the trouble of implementing rounded corners in unsupported browsers.border-radius): there were some differences in early implementations, but that was quite a long time ago (Firefox 3.0); current versions of all browsers that support it are pretty much the same.