If you run a 64-bit OS, then yes. It will give the other stuff running (the OS and/or any other stuff running along side) more room to work with without cannibalizing the available memory for Skyrim.
Since I'm using a laptop, is that at all prohibitive to upgrading? Like, for example, I know that I can't upgrade the graphics card without buying an entirely new laptop -- is the same true of RAM?
Not for RAM. You just need to check to see if your laptop supports more, like any computer. Once you do that, it's really a simple matter of opening the door on the bottom and dropping it in.
The only reason for any computer to only have an odd number such a "3.8" GBs of RAM is when any part of the video graphics available is some sort of onboard entry level substitute for the real thing, most likely the smoke and mirrors trickery that Intel prefers to foist off on unwary shoppers. Intel doesn't give their integrated chip any memory of its own, so it steals from the main memory pool.
nVIDIA make a lot of laptop GPU devices that have had half of their functions either omitted or else deactivated. They use Intel's chips to take on the duties of the removed first stage graphics functions.