I would never book through these sites. It is such a pain as MSPeconomist points out. My bet is that it's either some bulk inventory they've been allocated and/or it's not been updated and you'll get a 'this fare is no longer available' at some point towards the end of the booking. At that time of year IRROPS are very possible, and I'd rather deal with BA directly.

To your original question, yes, unless it's a tour discount fare or similar (not likely), you'll get TPs and Avios.