http://www.changiairport.com/changi/...ml?__locale=en suggests you can pick up a boarding pass airside.

In my experience, airside transit desks at Changi are painfully slow, so you can be better off nipping through immigration and checking in.

Note also that you have access to all three terminals as they're all interconnected by tram or on foot. Only some of the lounges in Priority Pass have alcohol on offer, if that matters.