Does the Gangplank tech of storing sheen proc in a barrel still work with Lichbane and triforce? Does the sheen proc transfer to chained barrels?

Was thinking about how much thebausffs likes to run AP on all his champs, and since he's been getting coached on Gangplank recently, I figure the next logical step is AP GP. But I've got no clue if either of my questions are true and i can't login to check myself in practice tool.

So wondering if lichbane proc can be stored like sheen? It has a 40% ap ratio+75% base ad, and barrels have 40% armor pen built in, so if it works, going ap isnt too much of a handicap. Also, you can go adaptive runes + dorans blade-> sheen opening items still for early game. And baus loves his passive healing on champs like gragas, voli, and cho. GP W with AP should be right up his alley.

Then I was thinking about how AP GP would play on a los ratones team comp. You could go symbiotic sole boots, and offset your resets to be shortly behind support/jungle roams, and just ult whichever lane the support/jung are ganking. The ult has over 100% ap ratio when upgraded.

Just some shower thoughts while I take my morning poo. What do y'all think? Completely bait build?