Your Guard CC has OPCON over day-to-day missions. The AD CC has ADCON so he deals with all of your awards and promotions etc. So yes, you are competing with everyone under the 19 AW which includes all of the LR units, and the TFI units at Cheyenne, COS, and Keesler. You or your Sq/CC have to get creative if you want facetime with your senior rater when it comes time for promotion, otherwise you might not actually meet him face-to-face at any point by virtue of being at a GSU.
As far as Sq jobs, the AD guys have their own duties like CCE/ADO/Tactics/Scheduling etc. The Guard also has their own folks in those shops. The AD and Guard Sq/CCs have offices right next to each other. So do the ADOs and DOs. When I left, the Guard did not really have a Sq/CCE (at least not a formal one), and they really felt they had no need for an OG/CCE, so an AD guy actually fills that spot. I did it for a while and really just ended up doing SQ-level CCE duties.