Eh i'd argue differently given that Hawke as said once before became Champion by removing the Qunari threat; you claim the Arishok was leaving on his own terms?
Considering he was effective taking over the city state, i'd say leaving wasn't within his terms period but we can come back to that.
So he takes the book and pirate back to Par Vollen, does that make up for the mockery his efforts have done the Qunari? He potentially kicks off a war with the Free Marches and Chantry, He loses hundreds of personal over the course of the battle and the preceding years all to reclaim a book that his own incompetence lost him originally.
I've been of the mind that Kirkwall was to be as much a repayment for his prior failure as the tome it self considering the Qunari lost it once before due to Orlais.
But anyway i'd say allowing the Arishok to walk away isn't indicative of Qunari support, it could be seen as many differing things from the all too popular apathy applied to Hawke to simple revenge against Isabella for abandoning them originally.
It's not just cooperating with the Arishok... it's handing Ketojan over to Arvaraad, not associating with mages more than needed, impartially enforcing the law throughout Kirkwall, maintaining a respectful tone with the Arishok and giving him frequent reports on Qunari-related issues, opposing Varnell, not hiding the abuse by Varnell's supporters... etc...
There is a pattern of behavior that can be established which coincides with the basic principles of the Qun: the strict adherence to order and the chain of command. If Hawke follows these principles as best he can within the culture and laws of of the human lands (specifically Kirkwall), then he is on the path to the Qun. His direct dealings with the Arishock can reinforce this, culminating in his agreement to accept the Arishok's terms for ending his aggressive actions in Kirkwall.
Obviously this is not the only explanation for why Hawke would hand over Isabela and the Tome, but it is a valid one... the possibility of Hawke being sympathetic to the Qun is supported by the plot, and is not confined to the realm of head canon and fanfic.
Now, whether or not the Arishok is going to face punishment when he gets home, I have no idea... I won't argue that the entire situation in Kirkwall was a debacle and he will probably be executed for the way things went down... however, none of that has any bearing on Hawke's views on the Qun, the Qunari, or the Arishok himself.