On-line information? That's another question entirely. This would be a more interesting test: can you make a basic webapp (or other type of app representative of your experience) without Internet access?
If you're dealing with an older stack and toolkit, you probably have many books' worth of manuals already installed. Unless you're unlucky and didn't notice the documentation isn't installing along with your tools. Or you're on Windows[0]. You can use them to work out most of the problems you're facing.
Newer tools though? There's this annoying trend of under-documenting things, and relying on people on StackOverflow to fill in the gaps. Or even worse, setting up a Slack/Discord for the project, and getting people to help each other there.
Maybe I'm just old, but when I'm working with computer tools, I prefer to solve the issues myself, instead of chasing around the Internet and talking to people. I also like to be able to continue to work when my Internet dies, or I'm out of range, or the site hosting the docs dies (happens more often than one would expect).
And to answer my own question: yes, I can write basic apps of the type I work on (and bunch of others, including games) without Internet access, as long as you let me use my computer - where I have access to heaps of off-line documentation and lots of prior source code to supplement it.
--
[0] - Someone at MS had the bright idea to ship PowerShell without help for its commands by default, so that the first thing Get-Help tells you is to download the man pages...