Too late for me. I already did it. It looked better without it but it doesn't look awful with it.

I've been thinking about that second surface I had to drill through to get the screw all the way in. At first, I was bothered by it. What was it? Why is the screw longer than the space behind the bumper? However, I have to believe that Chrysler knew how large that space was when they spec'd the license plate mount screw. It also seems unlikely that they would put anything vital so close behind the front bumper (the screw's only an inch long!). Going through two surfaces also means the screw will be more secure making it less likely to work its way out. So, for now, I'm going to assume that the second surface was just another part of the bumper and all is as it should be.