Absolutely, Alchemist takes place in the early 19th century and sets the stage for Jacket by establishing WWII, which leads to a global arms race that culminates in the US invading Vietnam in Jacket, which sets up the military obsessed themes in Panic. Watching Panic first is doable, but it's a lot easier to understand when you have the baseline story set up by the other two

There was a noncanonical alternate version of Alchemist called Fullmetal Alchemist: Brotherhood which explores a sort of alternate history where WWII never happened, and unfortunately it got more popular than the original series, which I think is what really causes the confusion with the watch order