As with pretty much everything in Arcanis, you are correct. . . and not.
Yes, the Orthodoxy would be interested in this magical item, but not for themselves. The magical box in no way brings the Twelve back together in the way the Orthodoxy wants, but it does expand on what they know. Who it mostly helps is the MOTHER CHURCH OF CORYAN (and to a lesser extent the Milandric Orthodox Church).
In terms of the Ansharan temple, the fact that it isn't pantheonistic is a strike against it in the minds of the Orthodoxy, and they'd most likely leave that detail to the Emerald Society (or the Azure Way), both of which are reasonably friendly with the Orthodoxy as their goals are generally aligned (though there is competition between the three for individual items).
In terms of the 'heretical cult,' was it heretical? The word heresy is a value-laden term, and it is actually possible the Orthodoxy may be interested in it as a relic of the First Imperium. After all, these Ansharans obviously represent SOME form of offshoot of the First Imperium Church. In this case, the Orthodoxy may in fact be interested in studying them than 'eliminating the heresy.' The whole "eliminating a heretical cult" angle would appeal to the Kalindruhl, Mother Church, and Milandric Othodox Church (and probably other religious factions as well), but not necessarily the Orthodoxy.
Basically, yes, the Orthodoxy would be interested, but not directly involved. Had you brought back Ansharan texts, they'd be interested. Had you recruited new members of the Orthodoxy, they'd be interested. They'd also be interested in obtaining the box, but so would any other Secret Society where a val'Inares could join so there is nothing unique there. In fact, that would be more of a nationalistic issue to control as gates aren't exactly stealthy, so it is of little use for a secret society who already has major control over these portals due to their Ansharan members. Better to give it to the Coryani Empire/Mother Church, and they can use them all the same.
The political aims of a lot of these groups is never entirely cut and dried. There are always countervailing arguments to be made, and strategic choices based on politics.