Well, controls aren't responsible of managing CSS source files and its addition to the page, so, the easy answer is no, you can't do that.
By the way, there's some solution for doing that.
You can include a CSS file with style HTML element from your control by adding a server control (HtmlGenericControl, for example), with the apropiate attributes and values, so, if container control requires some specific CSS file, you can add it during container control's life cycle, just before rendering it, to HTML head element (marked with runat="server" attribute) of some ASP.NET page.
Maybe a good way of doing that should be creating a configuration section in your web.config implementing your own one which may support creating dependencies of controls/pages and CSS stylesheet files, so, using this approach, you would be able to implement some method in a derived from System.Web.UI.Page class that may add CSS files depending on controls:
<cssDependencies>
<control type="YourNamespace.YourControl" cssFile="~/Styles/Default/YourControlStyle.css" />
<cssDependencies>
And then, your CustomPageBase would have its own "AddControl" method which should register its type in some collection that may be iterated in the PreRender method, so, there you can add CSS files based on control's types.
I'm just giving you ideas! :)
EDIT & NOTE:
Anyway, this approach, and your goal, could have problems in terms of performance optimization.
Best optimized sites should combine all needed CSS into one, so browser should load one instead of many during page renderization.
I believe combining all CSS files into one can be achieved with "CSS files and control types approach", and I would suggest you to go this way, because if you don't do that, you can end with pages having dozens of style elements.
Have you heard about DotLess project? Check it out here: http://www.dotlesscss.org/ Maybe it can give you a better approach with less effort!