Does a DB connection prevent AWS Aurora Serverless from pausing its compute capacity?
I believe you are correct, a single long-running connection will prevent AWS Aurora Serverless from triggering the pause-and-resume feature.

Aurora Serverless v1 can also scale to zero capacity when there are no connections if you enable the pause-and-resume option for your DB cluster's capacity settings.

Source: How Aurora Serverless v1 works
Take this with a grain of salt, though, as I haven't tested this behaviour myself, and the docs aren't perfect. The same doc goes on to reference &quot;no activity&quot; without defining it:

You can choose to pause your Aurora Serverless v1 DB cluster after a given amount of time with no activity.

Which begs the question: &quot;does an idle connection count as activity?&quot;
I think the best hint that an idle connection counts as &quot;activity&quot; is that the moment a connection is needed, Aurora Serverless resumes:

If database connections are requested when an Aurora Serverless DB cluster is paused, the DB cluster automatically resumes and services the connection requests.