Is it possible to add a value anyway? Well, you could stick a value= attribute in, but virtually all browsers will ignore it. Why? Because (ta-da!) it's a security risk! (It's the user's security that is at risk here.)
A bug with some early versions (early-mid 1990s) of Netscape allowed a value to be set: it was soon being exploited maliciously.
So you're free to add it, but it probably won't make any difference.