I have a core duo system with DDR3 RAM 2 GB. My motherboard says it can handle 8 GB of RAM. My question is if I add 8 gb RAM to system will windows7 32 bit support it?
No, it won't - 32bit OS can only use 4Gb RAM. And some of this will be reserved for the OS, giving you about 3GB RAM for your programs.
You need a 64bit OS to use more than 4GB RAM (assuming the software is also 64bit).
Furthermore, as per Michael Kjörling excellent comments, "Even if you use only 32-bit applications on a 64-bit OS, each application can get its own 4 GiB virtual address space. So even such an environment can benefit from >4 GiB RAM."