In a word, no.

In order to get to the AC at LHR, you'll have to get to the T3 departures area. In order to get there after arriving on AA, you have to go back through flight connections at T3. Unless you have an onward BP for a flight departing T3, they won't let you through.

One time last year I was connecting BA to AA at LHR. I made it all the way to the AA transfer desk in the T3 departures area, only to find out my onward connection to JFK was cancelled, which forced an overnight stay in London till my rebooked flight the next morning. The only way I could exit the T3 departures area, without taking a flight from T3, was to get escorted out through a series of locked doors by an airport official.