Well, because of those two items which are useless without stacks, this build is a sort of gamble. U need kills, lots of assissts to be usefull in team. If u die twice you are becoming useless because you lose almost all of you`r stacks.

This build would be good for stomping pubs, but I don't see how it could be viable in higher tiers of gameplay.

Calling it Advanced Build is misleading.

Because high elo players don´t die all the time. Stackable items are meant to capitalise on an existing advantage. In an even Game stackeritems are at best comparable to the normal alternatives. Good Teams will gank you before your Snowballitems go out of control.

Shen somewhat works as Carry because he is durable. He doesn´t work because he is slow and his chasing mechanism is not the best. He has the basestats but outside of that NOTHING on him scales with attackdamage, crits or attackspeed.
AP Shen might be viable with the rework on the TR. Basically they made Feint not worthless, instead of being a single source HP shield it reduces all damage by a flat amount (might have AP scaling) for 2 seconds. The top rank is 200 less damage for 2 seconds at 5 second base CD for 45 energy. With this he can tank even without Tankitems if he is good with timing.

Vorpal is a decent nuke with AP since it has a 0.65 scaling on the damage which is a lot on an ability with 3 seconds base CD. It also has a 0.2 scaling on the heal which is often underestimated, 70 HP over 3 seconds equals 116 HP/5. It´s not instant but the amount over Time is comparable with "real" healskills.
He also gains a much better Shield for his ult. AP Makes him much better support while not sacrificing all that much Tankiness, it´s harder to play though.