As far as the loyalty of Cassians in Avalonia goes, there has been the utmost effort to cultivate loyalty to the state among all citizens, and loyalty to the Cassian or any other church as a secondary loyalty has been tolerated. Loyalty to the Holy Nations != loyalty to the Cassian Church, and would be exactly the sort of thing that prevented Cassians from being equal citizens in past and hopefully won't in future.
As far as covertly goes, you say that these people are going to Turtle Island and the ships stop in on South Calzone while they're there as part of the ongoing effort to reclaim important stuff from the havoc that is South Calzone.
To be clear, I view South Calzone as already lost. I'm just trying to make the Holy Nations pay as dearly as is safe for the New Union for their invasion of land which the New Union had obvious plans for.
As far as loosely Spartan, I'm not familiar enough with Greek culture to give a definitive answer, nor do I have the time at the moment to do research on the matter. Suffice to say that there has been a long standing political/cultural/historical basis for this sentiment in Avalonia, and if it resembles Sparta, so be it.
South Calzone, lacking any central government, issues no response. Many factions, seeing the increasing force from the Holy Nations, consolidate and put up some weak resistance. Other factions disband or go underground. Quite a few on the borders simply leave and become bandit groups in different territory, causing traffic along the Argent Dabo road and other smaller trade routes to become increasingly dangerous. Many people seem resistant to conversion to the Cassian faith, associating it with the dark times of the dictator, while many zealots formerly expelled from Atensia or Avalonia already wholeheartedly accept it, but generally dislike the Holy Nations', and particularly Atensia's, involvement.
Also, South Calzone was a part of the Avalonian Union. All its weapons are Avalonian. Suspecting Avalonia of current involvement is like suspecting Russia for involvement in a former Soviet state because because military forces there are using Kalashnikovs (setting aside the Ukraine's position these past few months).