No it would not, windows 7 minimum requirements are
- 1 gigahertz (GHz) or faster 32-bit (x86) or 64-bit (x64) processor
- 1 gigabyte (GB) RAM (32-bit) or 2 GB RAM (64-bit)
- 16 GB available hard disk space (32-bit) or 20 GB (64-bit)
- DirectX 9 graphics device with WDDM 1.0 or higher driver
So it will run very, very slow. You must buy at least additional RAM. Keep in mind, that these are minimum requirements, so you want be happy.
I have never installed Win 7 on such bad configuration, but I have done it on virtual machine and it was too bad.
I know that this is a matter of personal opinion, but if I am stuck with that computer, I wold try with lubuntu, or some other lightweight linux. If you are using computer for web browsing and watching videos, there is no reason why you shouldn't give ubuntu a chance.