Seems very optimistic, to me. Smoker only cuts the attack to 9000 which is still almost all of most Gear Third teams' health. Alvida turns it to 3600, so it's a total of 12600. That's more than my Gear Third team's health, that's for sure. And since you need to focus on perfects, not recovery... yeah. I have all those units but I probably wouldn't try that myself. Too risky.
G3 isn't incapable of healing. Prioritize the first three Perfects the same as usual, then use those with meat and target Greats. Not as high in terms of damage output, but still achieves both aims.
But hold on, I've solved the missing piece: Mirage Tempo Nami. Negates an INT attack on a 15 turn CD.
Turn 1: activate Alvida, take 3600 damage
Turn 2: activate Ussop (boss timer now at 9)
Turn 3-9: G3 Luffy works his magic (boss timer goes from 8-2)
Turn 10: activate Nami, laugh at Rainbow Dragon
Turn 11-15: Ussop should refresh in this range, extending the timer by another 3
Turn 16-18: Alvida has refreshed
Turn 19: activate Alvida again
Turn 20-24: free damage
Turn 25: Time's up. Either it's dead, or you are.
G3 Luffy, Alvida, MT Nami, Ussop, ???
??? being any high damage unit, PSY preferred
You only need 7201 HP, and enough output for 2 million damage over 25 rounds.
EDIT: If Nami has at least 1 skill up, she should be available again on 25, extending another 6... which makes Ussop available again, so even if you don't achieve any healing (which makes Alvida available again... and keep extending the combo), that buys another 9 rounds to 34.