Yes, its possible to do that.
Call the remote request function when the text field loses focus.
Something like this..

Code: JavaScript
function CheckUser(username)
 {
    //... do the checking here..return true if exists
 }
 
 inputfield.onBlur=function()
 {
    if(CheckUser(this.value))
    {
       alter("This username already exists");
     }
 }

Happy coding!