Add AG Database Add process results in Connectivity Fail
Adding databases to an AG group does not disrupt interactions with the database

If you're adding a new database to an existing AG group then there will be no loss in service to SQL Server whatsoever--no severed connections. SQL Server does not need exclusive rights to the database in order to add the database to an AlwaysOn replica. The majority of what's going on behind the scenes on the source database is a database backup and log backup.

There will, however, be an I/O and CPU performance hit for backing up and copying the database and logs to the SQL replica(s). The bigger the database, the bigger the I/O impact. This may affect the performance of your connected application(s) if the database is large.

Note:
Although you may not experience disconnects to the database(s) you are adding to AlwaysOn, you are not using the listener for that AG group either. After you add database(s) to an AG group you will probably want to change the application connection strings to point to the AG listener rather than the SQL Server directly. Doing so will most likely disrupt service.