If the original inhabitants of Covenant have been killed, any remaining turrets in Covenant will be hostile towards new turrets, the player character and hostiles.
If you destroy the institute, the covenant quest chain no longer starts. You need to acquire the settlement earlier in the game.
Inside Covenant, players can find a few things that raise suspicions, like an abandoned bed roll, a note that talks about the rules of Covenant and how not to talk about Synths, and self-help books. Yet, none of this leads to concrete evidence of the fate of the caravan's survivors, or Covenant's involvement.
The Institute may do wrong, but they have the resources to literally rebuild what was lost in much less time than any other existing faction. If you destroy that, you could set back humanity's progress by a huge amount, if not destroy it's chances of ever recovering from the Great War.
It is impossible for the player character to fail the test. Unlike other settlements around the Commonwealth, Covenant is surrounded by tall concrete walls sprinkled with defensive turrets, and the houses and the yard are in pristine condition. The Sole Survivor even mentions how everything looks almost pre-War.
Take The SAFE Test Players can answer these questions however they would like, whether their responses are cruel, compassionate, or neutral, it does not matter, as there is no way for players to fail the test.
The SAFE test is a screening entrance exam required to gain entry to Covenant and is used to monitor those who pass through the settlement. Officially, its purpose is to keep the "undesirables" out, however, its true purpose is to root out potential synths.
You should be able to talk to the guy sitting in front of covenant, named swanson. He gives you a test, and once you past that test (it's impossible to fail) you can enter covenant.
Visitors to Covenant are subjected to a psychological test, called the SAFE test.