Will desktop DDR3 RAM work with a Xeon E3-1230 v3 processor?

Yes. The Xeon E3-1230 v3 uses the same LGA1150 socket as Haswell desktop chips and runs on standard consumer motherboards (H81, B85, H87, Z87) that only accept non-ECC DDR3. You only need ECC if using a server or workstation board with a C22x chipset. For a budget build, just buy the cheapest 16GB (2x8) DDR3 1600 non-ECC kit you can find.