It should do fine, but I would recommend that you look at getting 8 GiB of RAM.
Running a Windows 7 VM with 2 GiB allocated to the VM is pretty much a minimum. And not because Win7 needs 2 GiB to run, but because it runs a lot faster with 2 GiB because it will cache files in RAM. Since real disk IO in a VM is (in practice almost always) noticeably slower than real disk IO in a real machine, the benefits of caching can be more noticeable with a VM.
If you want to run more than one Win7 VM, 4 GiB will be very tight.
Right now I have a Win7 VM on my Win7 system. The VM is allocated 7 GiB, and it reports
- 498 MiB free
- 2697 MiB in use
- 2943 MiB cache in use
The 12 GiB host reports
- 215 MiB free
- 11023 MiB in use
- 1017 MiB cache in use
Everything will work fine with less memory, but it's a lot "snappier" if you have the RAM available.