Is it possible to force fullscreen in any application in elementary OS? I use Vim in my everyday work, but I would like to use gVim, but I don't see a way to make gVim fullscreen.
You definitely can for gVim. I think this works on most apps, including ones that don't have a full screen mode, for example System Settings.
Open up System Settings and click Keyboard and then check you are on the Shortcuts Tab and Windows is selected in the sidebar:
Then click on the "Disabled" text in line with the Toggle Full Screen and press a shortcut key of your choice.
I went for Ctrl + Alt + 9 as it worked in gVim. You could go for something else, but I'd advise against F11 - or any Function key.
Then you can easily toggle full screen on any app: