The suspension module or "brain" will go to sleep an hour after the ignition is turned off, so removing the battery won't affect the air suspension in any way.
If your not going to crank the car up every few weeks, keep in mind that even though the system may not have any leaks, because of the temperature drop, the car will probably lower. Because of this, the absolute best thing to do, is to turn the suspension switch off and put the car on jackstands. After you get it on the stands, do some preventive maintenance that will most definately extend the life of your struts/spring. With a clean dry rag, wipe the bladders of the struts & springs to get any loose dirt removed(no cleaner). Then spray the rubber down with spray silicone. For the areas you can't get to, wet down a rag or sponge with silicone and wipe that area down by hand.
As far as the compressor goes, depending on what manufacturer/remanufacturer you used and what type of dessicant material they used, unless the inside of your system looks like the titanic, you "should be" o.k. (Someone out there puts paper towels inside their dryers)
