Pete walks down a hallway, armed with a baseball bat. He looks into an office. And as he does, Jack appears from a door at the end of the hallway and slips around a corner.
My intention is that Pete doesn't see Jack because he (Jack) runs out of the room and around the corner in the hallway while Pete is looking into the office. Does "And as he does" make that clear?
It is almost clear. "And as he does" is clear (though some will have problens with using "And" to begin the sentence). There might be problems with using "appears", because it suggests that somebody saw Jack. If you are writing a play that is good, because the audience sees him. Otherwise it could suggest Pete saw him, so "comes out through" might be better than "appears from".
And should not be used to start a sentence. Periods in English are used as a short pause. You could easily make this sentence more readable by using a word such as "suddenly" or "simultaneously" if you want to be exact on the time frame in which Jack responded to Pete's movements. Add unnoticed at the end if you want to be extra sure that the reader realizes that Jack was not seen.
EX, Pete walks down the hallway, armed with a baseball bat, he looks into an office. Suddenly, Jack appears from the door at the end of the hallway and slips around the corner unnoticed.
I am not a native English speaker, so you could consider my answer not to be 90~100% idiomatic.
When I read the example sentence you raised here, I felt, in this part of "He looks into an office. And as "he" does," that "he" was at first thought to be as "Pete" before I looked at the Jack that follows immediately and after I saw the "Jack", I knew the "he" was a "Jack".
So, I'd recommend that like this: And his friend, Jack, as he always does, appears ~.
