Yes and No... Yes you can install the x64 version of Win7 on your computer, but it'll require you reinstall the entire OS and all apps. Some people might still consider that an upgrade, so pick your answer based on what your opinion is.
Personally though, until you get to over 4GB of RAM, there's really little to no benefit. So unless you're planning on adding more RAM at some point, there's little to no point.
I've built a rig almost from scratch and I have these kind of specs:
Cpu-
AMD Phenom II X4 B44
Memory -
Mushkin Enhanced 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1066 (PC3 8500)
Motherboard -
BIOSTAR A870 AM3 AMD 870 SATA 6Gb/s ATX AMD Motherboard
Graphics Card -
nVidia GeForce GTX 470
I want to know if I need to update my BIOS, and necessary steps to upgrade. Thanks in advance!
Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic