No. You can only save a map if it is a dungeon made in ‘DUNGEON BUILDER PACK’ with the dungeon builder tool. In this case, it will only save the last dungeon made on the panel displayed to the next session. 
Token positions will never be saved, only the dungeon tiles positions. This function is really complex and a patreon was oppened to see if users would contribute so that function could be added, but the goal to implement was not reached and still isn’t.