Anything can be done if cost isn't an option.
Chances are you're going to have three pop rivet or screw holes in the bumper. That said, some dealers just use two.
If you're lucky, the rivets will come out clean -- allowing for a pretty straightforward patch, prime and air brush paint and clearcoat job. The job, by somebody good, is going to run around $200 to $300 -- if your car has a non-metallic paint job. If your car's metallic -- add another $100. If you're serious and want to do the job right -- have the skin completely reshot -- although you're at $700 and will have an increased rate of chipping and stone damage no matter who does the job. In my experience, factory applied paints seem to hold up better than any aftermarket application.
If you're unlucky, the pop rivets will cause some deformation of the area surrounding it. This can be about the size of a dime in severe cases. That will require some sanding before the patch, prime and paint. Probably won't cost any extra to do this -- but it's just more work.
Bottom line? I'd leave it alone or use a couple of nylon stem bumpers. The reason is matching the paint and clearcoat. My car's yellow -- and there are four slightly different versions of it -- even though the paint codes are the same. Heat, humidity and a bunch of other factors can influence how a paint sets up. Hitting it just right with an air brush, unless you spend the money for a top notch person, can result in either a slightly different color paint -- or a slightly foggy finish in the clearcoat.
As far as stem bumpers are concerned, these are little press in inserts that will fill the holes -- but leave little bumps on the bumper. You can paint them to match. Yeah, it's a punt -- but you get used to them after a while. Certainly better than a goofy looking license plate you don't want or a crappy air brush job.