The thing about "people watching them"... well yes and no.  No one is assigned to go out and watch the new kids on liberty.  However, you're near a huge Navy base.  There's a lot of sailors, staff and student sailors.  Any Navy service member who sees a new sailor acting incorrectly in uniform is allowed to walk up to the new sailor and correct  their behavior.  Usually it is simply a friendly reminder.  They don't have to be their boss, or in uniform themselves, they just have to be Navy.  Pretty hard to be anonymous near Great Lakes or even in Chicago.   Happens less in the fleet, but by then, most sailors have the hang of how to act so they don't draw attention to themselves.  

Think of it this way, your sailor just busted his ass to have the privilege of wearing the uniform of the greatest Navy in the world, to represent his country and all Americans.  He is now a professional service member.  You want to honor his hard work and service.  He isn't all yours anymore, when in uniform, he belongs to all of us.  Very prideful thing.  So that may make it easier to keep the PDA limited and in the hotel room, and be happy about it.

I believe that they can link arms.