The following observations exclude self-built, custom-built PCs and only deal with off-the-shelf OEM products.
A few years ago, the OEMs finally split the prices between general use (i.e., no separate GPU) and gaming/high-end video processing (i.e., separate GPU chipset). Before this happened, the prices for PCs were a fairly continuous spectrum, but afterwards, a clear split in prices became apparent.
The price you mentioned would be for a general use PC (no separate GPU) regardless of it being a desktop or laptop. This would be okay for most school use excluding any work you may have to do if you are majoring in gaming or some form of high-end video processing (e.g., CGI art production, animation, etc for film). It would not be the type of PC you'd want for gaming, though, and probably would not run FO4 or would only run it with low specs and great difficulty.
It is far better to spend the extra money and get a higher end gaming-specific PC because you can do both general use work such as office productivity as well as high-end work such as gaming or video processing. Having a separate GPU chipset that is specifically designed to perform video processing and lessen the load on the CPU is always going to be a better choice.
Gaming laptops usually start around the $1000 price mark. As I said, there is a clear price split between general use PCs and gaming PCs now. However, you can get an ASUS gaming PC that is very powerful from Best Buy or other retailers for about $1000 and it should do pretty much anything you want it to do, including running FO4 at very good specs, perhaps even ultra mode. I'd recommend making sure that you get one with the Nvidia GPU because they seem to perform better. I have two ASUS gaming laptops, one with a 260M GPU and one with a 560M GPU, and both of them run Bethesda games on ultra mode with high-end graphics mods with no trouble at all (well, aside from the typical crashes due to mods, of course, but that cannot be avoided).
I seriously doubt that FO4 will require a 600+ series Nvidia GPU, but the 640 (and 640M for laptops) is probably the lowest price you'll find today in ASUS OEM laptops. My laptops are a few years old so they have older GPUs, that's all, but it has never been a problem (not yet, of course).
Edit:
Basically, it is worth it to invest the money now rather than attempt to push a PC that just isn't intended to be used for high-end software. As an anology, you don't try to race cars with a typical passenger car because the latter car's hardware/mechanics just is not intended for such high-performance work.
Also, there is a long-standing and still-prevalent myth that desktops are superior to laptops for gaming, or even that desktops are required because laptops simply can't handle the work. This is false and has been false for many years now (maybe since about 2007 or so). Rather than a concern about laptops running games as well as desktops (which they do and have for many years, as long as you compare gaming laptops to desktops), the question is whether or not you want/need portability. Some people don't need to be mobile so a desktop is okay. However, many people really need to be able to be mobile, including the freedom to game wherever they are, so they need a gaming laptop because they can't lug their desktop around everywhere. The higher price for gaming laptops today is mainly due to paying for the freedom of mobility for high-end work rather than being able to do the work at all. You can pay less for a desktop to do the same work but you won't be mobile.