Not even. They'll just drive without a legal license. Hell, most of them already do. It's not like illegally crossing the border suddenly incentives you to wait in a DMV line, or pay for auto insurance so you can get a drivers' license legally.
They don't want to be a legal citizen. That's why GWB's premise is wrong. These illegals want to exploit the system. After they pass this disaster and no one registers, is GWB going to then call for deportation??? No. I don't think so.