Do people forget where something protected by the Fidelius charm is, if the spell is cast after they already know this location?

Question

As a simple example - lets say that someone casts the Fidelius charm on a public building like Hogwarts or the Ministry of Magic.

Will everyone (so LOTS of people) immediately "forget" where these buildings are?

Answer 1

While not stating it straight out, it appears that you can remember where-about the house was, but you'll not be able to locate it anymore.

Professor Flitwick cleared his throat.

‘An immensely complex spell,’ he said squeakily, ‘involving the magical concealment of a secret inside a single, living soul. The information is hidden inside the chosen person, or Secret-Keeper, and is henceforth impossible to find – unless, of course, the Secret- Keeper chooses to divulge it. As long as the Secret-Keeper refused to speak, You-Know-Who could search the village where Lily and James were staying for years and never find them, not even if he had his nose pressed against their sitting-room window!’ - Prisoner of Azkaban

This is implied that should Voldemort know that James and Lily lived in Godrics Hollow, it would still be impossible to locate their house, because of the magic that protects it.

Even later in the series we have Death Eaters/others hanging out in front of the Grimmauld Place, because they know where it's supposed to be, but can't see it.

Barely a day passed without one or two people arriving in Grimmauld Place with no other purpose, or so it seemed, than to lean against the railings facing numbers eleven and thirteen, watching the join between the two houses. The lurkers were never the same two days running, although they all seemed to share a dislike for normal clothing. -Deathly Hollows

Since knowing the location is possible, it's unlikely the spell would cause you to forget it.

Answer 2

Yes

From Pottermore:

The Fidelius Charm is extremely ancient and still used to this day. It involves the concealment of information inside a living person. The chosen person, or Secret Keeper, is the only person who is thenceforth capable of revealing the protected information to others, however many previously knew it.
_{(Pottermore, "Secret Keeper").}

This is in keeping with Himarm's answer. It seems that the Fidelius Charm induces forgetfulness about the specific location that's being protected. You'd forget where a location was and be unable to find it, even if you were very familiar with it. As Pwassonne says, there wouldn't be much point in it otherwise.