Not necessarily, it would be up to the other *A carriers policy if they check through separate tickets. UA will do it under their policies, but there is no *A requirement that a *A carrier check through to another *A carrier on separate tickets.

Ignoring that it would also be unusual for OP to be arriving in AUS on a *A carrier to then connect to a separate ticketed UA international itinerary, since it would imply they're arriving from an international point in AUS.

Still would be worth researching if whatever OA carrier they are on though checks through separate tickets to UA, since some will still do that (usually depending on your status with the OA carrier)