If you conquer Forgotten Monument before turn 3 does it count as a conquer for triggers etc?

No, you cannot conquer Forgotten Monument before your third turn, so it cannot count as a conquer for any triggers.

According to the card text of Forgotten Monument, "Players can't score here until their third turn." Because "Conquering" is a method of scoring (Rule 464.1), you are prohibited from performing a Conquer action on that battlefield until the condition on the card is met.

If you attempt to move a unit to the battlefield before your third turn, you will not be able to score or conquer it, and therefore no "When you conquer" abilities will trigger.