Do 32 bit applications take advantage of >4GB of memory?

Question

As a general rule, does an application written and assembled on a machine which handles 32bit wide instructions, see any benefit from memory addresses after the first 4GB? Suppose a 32bit application used 1GB of RAM, and I opened 5 instances of this application- can all five instances sit in memory on a 64 bit OS with more than 4GB of memory? Or can the application not see the rest of the memory the OS can? Not sure if I have asked this properly, I'm a student just starting to learn this stuff.