Can someone clear post while on PCS leave?

If you are staying at Drum while he goes to Korea, it's pretty easy to clear. If you're moving, he needs to arrange HHG as far out as possible. They dictate when they are available to pick up your HHG not the other way around. You have to be available on their schedule which is usually something like this: "Be on Standby Wednesday through Friday, 0800 - 1700, that's your window".

So I am going to guess that you have already received your "No Fee" Passport (government issued, not purchased) with Sofa stamp. But I wouldn't clear while on leave. If I am remembering correctly, Ft. Drum issues clearing papers 10-14 days prior to departure. Additionally, part of the final out process is the finance portion where they put you in a transit status for pay and entitlements. One thing to remember about CSP is that there are three different answers to the request 1. Concurrent: Meaning you fly with your spouse or within 60 days of there arrival. 2. Deferred: Meaning housing is will not be available for 61-140 days after spouse arrives, which means you would have to wait in the states, and once housing is available, you would receive a separate set of Family Travel orders on, to ship HHG's and POV on. 3. Denied: Which means just what it says. At that point the spouse can request a deletion from the assignment or serve an "All Others" tour (12 months alone). AR600-8-11, AR 55-46, AR 614-30.

Getting back to the Passports and Visa's. Based on the Foreign Clearance Guide (FCG), you must apply for your Special Issuance (No FEE) Passport with the installation, and if it doesn't arrive in time to meet the flight time, then you can use your Tourist Passport. But you will need something from the Post Passport Office showing that you applied for the official. Additionally, if you plan on doing any travelling while there each family member should have a tourist passport as you cannot us the Official for leisure travels.

Its been a while, but while I was on PCS in the Navy in the 80's I left the post often. I flew commercial from my Duty station, to my home, to Hong Kong, to my new Duty Station.
While at the port of call of my Duty station the USS Longbeach, I traveled around town seeing the sites, slept in the base enlisted mens quarters and ate in the chow hall.

While you are on Leave, you are free to do what ever needs to be done to serve your needs. After leave is over you serve the needs of the Navy, Army, Airforce etc.