I wouldn't expect you'd have any problems, as long as you have the appropriate passport or whatever you need to enter the country. There are all kinds of reasons to go outside of security at an airport. As long as you are checked in and show up on time for your next flight, should be fine.

The train is very easy, maybe 15-20 minutes to Centraal. From there it's just a few minutes to walk to the Jordaan, or down Damrak, or wherever you'd like to have lunch.