Not really. The C# method is called in code-behind (you are using ASP.NET), and that gets called only upon page reload when the server executes the back-end code to form the updated page.
What you could do is to have the server-side code (the C# code) generate client-side JavaScript that would then be executed as the page reloads in the user's browser. That code would then be executed, of course, after the server-side C# code. See Inject Javascript from asp.net code behind files for an example.
Another option would be that you use AJAX to call the server-side code (so instead of code-behind). Then you can determine the sequence yourself. For more on AJAX with ASP.NET, see http://www.asp.net/ajax.