No.
You could write your own methods to use embedded resources and generate html to write them to the page.
As a best-practice approach, though, I wouldn't recommend this. You should have a clear separation of style and markup. If you want to write a custom control that is dependent on a stylesheet, then I suggest that you provide a default css file along with your control.
EDIT (to answer questions in the comments)
You can run this code to add a reference to the CSS file to your page (at runtime). Note that because you're using the RegisterClientScriptBlock method, you can manage insert duplication. Here is an excerpt from the link for the method:
A client script is uniquely identified by its key and its type. Scripts with the same key and type are considered duplicates. Only one script with a given type and key pair can be registered with the page. Attempting to register a script that is already registered does not create a duplicate of the script.
StringBuilder sb = new StringBuilder();
sb.Append(@"<link rel=""stylesheet"" type=""text/css"" href=""");
sb.Append(this.Page.ClientScript.GetWebResourceUrl(this.GetType(), resourceName));
sb.Append(@""" />");
this.Page.ClientScript.RegisterClientScriptBlock(this.GetType(), "MyCSS", sb.ToString());