Australia is currently trying to do this with revil over the Medibank breach. It will be interesting to see the outcome.
No it won't. We are totally toothless here. A few ignorant politicians trying to score points by sounding tough in the media isn't going to make any difference.
Once a case is raised in the system they're flagged for Interpol and a European equivalent. It makes retaining them at a border simpler. There's no downside to filing a case and there might be an upside in the future.