No, 32 bit programs can only access 2 GB of memory, this is under a 32 bit system, some can with special setting (boot.ini) acces 3 GB. Theoratically the OS can adress 4 GB of memory but this also includes videomemory and hardware buffers, so you see many 32 bit systems wih 4GB installed only showing 3,5 till 3,2 GB available!
When using 32 bit software on a 64 bit os, the software should be able to acces 4 GB of ram, that’s it! It’s a limit of 32 bit addressing.