Almost certainly yes, but you need to check with STA that they are not selling you a consolidator or bulk travel fare, which don't get Avios / TPs. So find out the fare basis code or fare bucket. But it is unlikely from STA to sell these tickets I suspect. Furthermore I'd wonder if you can't find the same fare via BA or hunting around AA / US. As a very, very general rule, their computer systems are sometimes sophisticated enough to find fares that the airline systems seem to eek out with much greater difficulty, but they can still be obtained direct from the airline if you look carefully (e.g. they may have combined two single fares, and/or bought from a different sales city). Proceed carefully with an OTA, since you can't easily change / upgrade their tickets.

Regardless of sales channel, it is currently the case that lower cost US metal/ticketed flights will get you higher Tier Points than BA or AA in Main Cabin on a similar fare, which is an oft reported glitch.