Was on BA299 last week. From the plane to a cab (including waiting for luggage) in about 20 minutes. So it's doable on a good day. The two-class ORD-LAX flights are probably not that tight in A class so I'd imagine you'd have no trouble waitlisting for the next day's flights should you end up missing the 19:45.

(Well, I should update my optimistic assessment to mention that were delayed on departure by about 1.5 hours as the U.S. didn't clear the passenger list for travel until that time.)