We do it all the time. I can type while talking to people. I can also read/process the text ahead while saying out loud what I read a few words back. We do a lot of things concurrently when dealing with text - I'm not staring at the cursor when writing code either.

(Unless you meant it literally. No, I didn't mean actual peripheral vision. Just noticing things beyond what I type.)

I did mean it literally. the solid angle covered by the fovea is tiny.

The eye also doesn't literally stay 100% static when you look at something.