The Intel® Core™ 2 Duo E4500 is a 64bit processor so yes it will support 4GB of memory. Now the motherboard and the OS both need to be able to support that amount of memory for it to be usable on your system.
Looking through all the chipset that are supported with this processor (except the nVidia) and at least the chipset will 4GB, that maybe change based on the motherboard manufacturer. If you let us know some more information on your system we maybe able to answer these questions.
Christian Wood
Intel Enthusiast Team