Based on a simple test I ran, I don't think it's possible to put an inline <style> tag into an ASP.NET server control. The style did not end up rendering to the output HTML. Even if it was possible, I'm sure it is bad practice to do this.
Is it possible to do this? I can see it being useful for quick prototypes that just have 1 or 2 CSS classes to apply.
Update:
Per Jonathan's request, I was going to post the code. But, when I opened my project and loaded the page again (just for kicks) it ran correctly. My guess is that it had something to do with restarting the ASP.NET development server that Visual Studio launches when you run a page.
In any case, when I included identical multiple controls on the page, I got multiple identical styles as well. This would probably be the explanation why doing this is a bad thing. Regardless, it is always good to know best practices and alternative methods of accomplishing a task, so I do thank everyone for their answers.