Your CPU is fine but 256 meg of VRAM is quite low for a game like Fallout. For any games these days actually. You should have at least 512 for most of the new games out there, preferably 1 gig. And the 4250 is on the low end for that series. So you can probably run the game but at very low graphic settings, and you'll probably still have to put up with alot of stuttering as you games swaps textures.
The problem will be made worse because of your low VRAM. Any textures and meshes the game needs will be stored there until there's no more room to hold anything new, then the video card will dump what the game thinks you don't need in order to load new graphics. Because you only have 256 meg of VRAM, this will happen more often than it would if you had a card with 1 gig of VRAM. Many of the textures of the game are quite large so it won't take long for your VRAM to fill up, which means you'll be doing alot of swapping of your graphics files.
Thats really a non-issue. 512 is more then enough for NMC's Texture pack, and that is like 2x the file space of the default textures, so 256 is just fine for vanilla textures. The biggest source of lag will come from the 5400RPM hard drive.
You could argue how much Ram and Vram you could use, but it comes down to what is actually needed to run the game. 256 is more then enough for the graphics settings he will be running at. If you really want proof of this, just keep in mind that an XBox plays at just under mid settings and only has 512 of total memory, where as the laptop the OP is looking at has 256 dedicated Vram as well as 2GB system Ram