For all intents and purposes, the answer is "no" (while there might be some obscure way of handling this, it's not the most optimal way).
It appears you are looking for a way to manipulate the HTML that is being produced on the server-side, which is a very legitimate desire, it's just that the approach on the server side using .NET (or other) technologies is radically different than how you would approach it on the client-side.
Because the content is already rendered on the client, the way you would apprach modifying it is different. On the server, the page is built of from various parts which ultimately render the HTML to the client, using data that the client doesn't necessarily have access to (as well as resources and libraries).
It's for that reason you want to use what's available on the server to accomplish what you are doing.
Whether you are using the WebForms model or MVC model of ASP.NET, there are mechanisms that allow you to bind to data without having to write out the tag yourself.
For example, in the WebForm model, you have the TextBox class which you can set the Text property on.
In ASP.NET MVC, there is the TextBox extension method on the InputExtensions class which allows you to pass the content of the textbox and the method will render the tag for you.