Does it run once per day when the user opens AR? Yes.

Since it needs exclusive use of AR data, can it be auto run after hours with a scheduled task? Yes, with Adagio Console installed which allows automation of many functions in all the Adagio modules. There's a webinar on Thursday showing this.

Can it be run once a week instead of once a day? Sure. The user has an opportunity to skip the process.

Can the On Hold style be saved so that it doesn't have to be re-selected every time? Yes. Defined a Filter with the Style you want for On Hold customers and give it a fairly high priority.

Does this all make sense?