Most important will be always carry a TP and instant TP to the place where your teammates got ganked or enemy diving for kill. This will change the game by a lot if you manage to save your teammate or get some good trades or even wipe them off.

Jugger ulti does 150-250 dmg per slash and just like his first skill, he can attack during his ulti. Nothing improves his ulti other than scepter. Why people say you can get more slah if u got more attack speed, means when you jumping, you can right click few more times more.

To answer your question, No for jugger ulti but yes they can proc during normal attack when jugg ulti.