AFAIK, you can't take any action on the button click for a policy banner, so no, there isn't an easy way to do what you're after.
I had at one time figured out a method of using the login policy banner and a way to remove it when conditions were met, but it was very specifically set up as a way to enforce our FileVault 2 encryption. Essentially, what I put together (and we never ended up using) was a LaunchDaemon & script that was able to check a number of conditions upon user login. If the machine was not encrypted, but the conditions indicated it should be, it would lock the user out of their account, enable FV2 with the Next User option, and auto logout. In the middle of all this, it would move a policy banner rtf file into place so when it hit the login screen, it would clearly state in that banner that they needed to enable FileVault when prompted, along with some basic instructions. This policy banner would then stay in place until the script being run by the LaunchDaemon determined it was no longer needed (user enabled FV2), then it would remove the file.
The reason I mention all this is to illustrate that it may be possible to remove it, if you can determine that a script can see that it was viewed once already and the user accepted the policy banner. Maybe check to see if the user account on the Mac has been logged into at least once? I'm not exactly sure what would make sense, partially because I don't know what your setup is. But there may be some flag you can look for that would help a script know that the policy banner should get removed from the system.
