No, it goes down the South Western Main Line, which I find odd personally, as I think they go along the Windsor lines on the other end of the station in reality to get to Reading, as going down the SWML it can't get there without reversing IIRC - maybe that track doesn't really exist properly?
Where does it go south of Clapham? The only place that would make any sense is turning off at Redhill to go to Reading via Guildford, but that's not realistic at all.
It goes through at a few different times. I've seen it a few times at other times of the day when running timetable mode.