Here's a method which I think seems to work system-wide and kills red underlining, overriding the way many apps annoyingly default back to "Check Spelling While Typing".
1. Open "Language & Text" in System Preferences
2. Under the "Text" tab, select Spelling... (which is probably set to "Automatic" by default), and scroll down to the bottom where it says Set Up...
3. in the box that comes up, uncheck every language. It seems to require that at least ONE remain checked, though, so I just left "Polski" (Polish?) checked. I don't think it matters at all which one you leave check as long as the English ones are unchecked? Anyway, I left Polish checked and this all is working great.
4. Click Done to apply the settings, and that main Text tab, leave Spelling set to "Automatic by language"
Once you do this, from what I can tell you can type anywhere in any app, even with Check Spelling While Typing set to on, and the red underlines won't appear. This is working for me, anyhow. I can type some gibberish like "lkjsfdkljhf" and it will not be underlined. If I go back in and check those language boxes again, type the same gibberish, it will come up underlined in the same app.