If you get an external USB WiFi then it should work just fine.
I can't say on if it will work fine, or if the computer itself will work fine, with the internal removed. While it shouldn't effect the external USB one, it could effect the computer itself. Some computers are quite moody if you do things like remove parts. The only way to tell for sure is to try. If needed, you can always reinstall it (until you can afford a new internal) and just use the external.
In the end, you can always use the external and never get a new internal. That part is up to you.