The Sims 2 only uses 1gb of memory according to my config log. Is it a good idea to install the 4gb patch with only 4gb of RAM? If not, is there a way to at least get it to use 2gb?

If it runs ok, I don’t see a reason to try your luck on this, to be honest.
However, you can always make a backup of the game executable, apply the 4GB Patch, see how it runs and decide if you want to keep it or restore the original.

Your computer only has 4gb of RAM, and other processes and services will need to use some of that while your game is running (even your operating system needs to use a certain amount of RAM). If you installed the 4gb patch, you could theoretically use all your available RAM with just the game itself. This would cause your computer to start running very slowly and inefficiently, as once your available RAM is used up your computer will use something called swap memory, which is allocated space on your hard drive that acts as RAM. This puts a lot of stress on your hard drive (especially if you have a mechanical drive versus a solid state drive), is much much slower, and will also generate many page faults, which is when a part of a program is stored in the swap file on your hard drive and not your actual RAM, and the program requests that part to be loaded back onto actual RAM so it can execute properly (which means your computer will have to switch around more files between your RAM and hard drive again). Again, this puts a lot of stress on your machine. Generally this is not something you want.

TL;DR: No, not a good idea. Don't do this.

I have the 4 GB patch on a laptop with 4 GB of RAM. My game never exceeds 1 GB of RAM usage, but I do have very little CC (mostly mods, roughly 0.5 GB).

No, there's no point. You can't give your game what your PC doesn't have to give. If you are on win 10 you will need most of this to run that. Instead, I would make sure you turn off unneeded processes when you start the game.

mostly as @joandsarah77 said, setting LAA bit is useful if the system already has got more than 3.7GB RAM. It won't break anything if you have got less, though.

The game shan't use more than ~1.0/1.5 GB RAM until you really throw a ton of high-poly/hi-res textured objects into the fry. And I mean "really" and "a ton".

For your own sanity sake I hope you are not using W10 on this machine...