Yes, the setting of the path immediately executes the move for that turn. Treat it as a manual move, if you like.
The next moves after that are all executed at the end of the turn after you hit the turn button but before the next turn starts. However, the eventual result is the same regardless whether you move your ship manually or using the path automation.
Count the turns it takes to reach the same destination result. Suppose you are moving a 4 mp ship to a destination 12 hexes away.
Option #1: Manual movement
Turn 1: You manually move the ship 4 hexes and have now traveled 1/3 of the distance. Your ship has no move points left. You hit "turn".
Turn 2: You manually move the ship 4 hexes and have now traveled 2/3 of the distance. Your ship has no move points left. You hit "turn".
Turn 3: You manually move the ship 4 hexes and have now reached the destination but your ship has no move points left. You hit "turn".
Turn 4: It's the start of the turn and your ship has full move points and it sits in the destination awaiting your commands.
Option #2: Setting a path to the destination
Turn 1: You set the path to the destination 12 hexes away. Your ship moves immediately 4 hexes and has now traveled 1/3 of the distance. You hit "turn".
Turn 2: Your ship has full move points left. You hit "turn". The ship moves 4 hexes and has now traveled 2/3 of the distance.
Turn 3: Your ship has full move points left. You hit "turn". The ship moves 4 hexes and has now reached the destination.
Turn 4: It's the start of the turn and your ship has full move points and it sits in the destination awaiting your commands.
--> The outcome from both options is that at the start of turn 4 you have a ship in the destination with full movement points and awaiting your commands.
You aren't losing anything by using the path automation.
(That is, assuming you set the path so that the path distance is evenly divisible by the movement points. Which you should do.)