Stacking Sensei's Divining Top Abilities
Yes, you can do exactly what you describe. You can activate Top's first ability, then, while that ability is on the stack, activate its second ability. Then the second ability will resolve, and you will draw a card, then put Top on top of your library. Finally, the first ability will resolve, and you will look at and reorder the top three cards of your library, including the Top you just put there.