Up until level 20 it does, yes.
When a new adventurer and a mentor form a party, they both receive a bonus to experience points earned from adventuring activities. This experience point bonus applies until level 20.
Bonuses to experience points earned will apply to the following:
Enemies defeated in the open world (leves, treasure hunts, etc.).
Enemies defeated in dungeons and guildhests.
Experience point rewards for completion of dungeons and guildhests.
Experience point rewards for completion of FATEs.