Yes you can. You just have to register the event handlers manually instead on having Visual studio do it for you. The code from my previous post will work fine, you just have to add this after you create the TextBox:

this.textBox1.MouseDown += new System.Windows.Forms.MouseEventHandler(this.textBox1_MouseDown);
this.textBox1.MouseUp += new System.Windows.Forms.MouseEventHandler(this.textBox1_MouseUp);
this.textBox1.MouseMove += new System.Windows.Forms.MouseEventHandler(this.textBox1_MouseMove);