I see your point there, that It increases Tresh's damage output, that's quite obvious. There isn't much MR in your build, GA helps the problem in late game, but It seems bit late.I'd recommend some more MR, unless enemy team is full AD or almost full AD.

Thank you for the colors recommendation I'll have to put that in as soon as I can. Also the reason why I build runnann's hurricane is for two reasons one when combined with frozen mallet given two other enemies are nearby we will slow three targets which can be helpful in team fights. Second I Get it because the damage from death sentences passive will also apply to two other targets
I know I said two reasons but a third is due to the increased attack speed we can increase our damage out put in team fights. Also since thresh is ranged he still benefits from runnann's hurricanes passive.

Use more colors, because colorless wall of text makes tired, and I am wondering why you have runaan's hurricane in your build? It's ranged (adc) item, not a melee item, but I am not going to downvote this build, eventhough your build could be better.