Yeah you can.
Try,
(HomePage.FindControl("YOU_CONTROL_ID") as TextBox).Text = "Any thing";
You might get NullException on runtime as because
HomePage.FindControl("YOU_CONTROL_ID")
or
HomePage.FindControl("YOU_CONTROL_ID") as TextBox
can be null. Add appropriate null exception handling get going with it.
I am not sure what type of ASP.NET project is it. You can change the access modifier of the control in Page to public and access like you said in your question if it is Web Application.