No, it does not. The presence of the LTCH verifies that you are not in violation of the law. The LTCH proves you did commit an infraction, which means there is no need for further questioning.
A LTCH proves....(maybe, see below)......there was no violation of the law in regard to the carrying of a firearm.
The pink piece of paper can be easily duplicated, and cannot be verified 24/7.
There may or may not be a violation of law, pending an officer investigation from a MWAG call.