Does a Tessary alert get dropped if a case opens during quiet hours?

No. If a case opens while quiet hours are in effect, Tessary holds the notification rather than dropping it, and delivers it once the window ends, stamped with when the case actually opened rather than when it was sent. The reasoning is that alerting exists so nobody has to keep the app open, and silently discarding notifications for a chunk of every day would quietly break that promise. Delivery cadence limits work the same way: if several cases open close together, Tessary batches and paces the notifications instead of skipping the ones that don’t fit the pace. Nothing about a case’s status in the product changes while a notification is held; it’s fully visible if you go look, and the hold only affects when the notification goes out.