You forgot an important part of Rule 404:
"Evidence of other crimes, wrongs, or acts is not admissible to prove the character of a person in order to show action in conformity therewith. It may, however, be admissible for other purposes, such as proof of motive, opportunity, intent, preparation, plan, knowledge, identity, or absence of mistake or accident, . . ."
That is worth repeating because they will use it to show character and they will do it under the legal premise of one of the other reasons.
They most definately will attempt to use it against you. That is thier job, to prove you are guilty. To do so they will provide examples of why you are likely to have made the decision to do what they say you are guilty of. They will create an image of your character favorable to a conviction.
A good defense attorney will simply make it a non issue. They will show that such a person is in fact more law abiding than the average individual, and give examples of countless upstanding and respectable people with such a permit.
To think a prosecutor or attorney will not use every fact available to thier advantage though is naive.
They will likely try that angle at some point in hopes that it tips the scales in at least some juror's mind.
Obviously you only got a legal license to have a deadly firearm because you wanted to shoot someone, wanted to be ready to shoot someone, and were looking for any excuse to shoot someone.
If you stopped to ponder what a prosecutor could say about most choices in life you would do very little. You would not be a free man. Living life and making choices comes with risks. You minimize those risks as an intelligent person, but you don't stop excercising your freedoms because of them.
A prosecutor would say the same about a person that kept a firearm at the ready for home defense if he felt it would help his case. Anything that the jury cannot relate to will be tossed in to help sway them his direction.
Since only a limited number of people have a license to carry a firearm, it is very likely he will feel that is an angle to include. The average juror will have no personal experience with legaly carrying, and it may be news to them it is even possible.