I know its below even min sys requirements but do you think I can still run it?

1G? Probably not.

I assume that is a Geforce GTX 650 card which is above minimum system requirements. It depends on how much effect video memory has on the game. Of course, RAM can be used for video memory on Windows 8 and newer.

Yes, It will run it just fine.

The Xbox One will run the game on high settings and it has a graphic card equivalent of a 7870 which is a low end card by the way. The 7870 happens to be the minimum requirements too.

So with that said, the minimum requirements for Fallout 4 are targeted around high settings that the Xbox One uses (just compare the minimum specs to the Xbox One). If you are above the minimum specs then you can most likely will be able to run it on ultra in some or all settings and resolutions.