For the JVM to fill all the heap, you'd have to generate enough objects that survive the young generation collection. That would be unlikely on the lightly-loaded stand-by server.
To improve your chances of catching all the garbage in the young generation, configure your young generation heap accordingly: larger sizes, more generations before objects age out. This is a compromise between confining your standby server to young generation and the collection profile you need in your primary server.
Update: the new G1 collector uses different configuration options. PLease look at http://www.oracle.com/technetwork/tutorials/tutorials-1876574.html to learn more. The option most relevant to your case would be
-XX:InitiatingHeapOccupancyPercent=45 - Percentage of the (entire) heap occupancy to start a concurrent GC cycle. It is used by G1 to trigger a concurrent GC cycle based on the occupancy of the entire heap, not just one of the generations. A value of 0 denotes 'do constant GC cycles'. The default value is 45 (i.e., 45% full or occupied).
IOW, the equivalent of young generation collection will start when the current heap (the min heap size initially) is 45% used up. Your light-load server should never leave the min heap size (unless it produces relatively long-living objects, in which case see -XX:MaxTenuringThreshold).