If the alert is acknowledged (and has been disabled/ removed from the property), it shouldn't impact anything else. It will still show up in the Alert Summary page as it shows historical data (same as Alert History) and there is no way to purge the Alert Summary at the moment (because the data displayed is an from in-memory and not from the database). On the flip side, Alert History is saved on a Stream, so that can be purged.
In any case, I have an enhancement ticket filed with the devs on purging the entries (and purging non-existent Alerts) from the Alert Summary table. I'll keep the thread posted on any updates.