Default Chinook on my server rarely drops the crate. It will do its normal path, but it never leaves the crate. Will this addon potentially fix that?

This addon could fix that yes, as the addon forces the chinook to drop its crate after a certain amount of time has passed and, depending on your config, all conditions are met.

Good to know. A few follow-up questions, then...

Would I set this to true or false?   

"Prevent the game from handling chinook drops": false,

This depends on the behaviour you want out of the chinook. If you just want the crate to drop more often, leave it to false. If you want the drop to be 100% random, change it to true.

I'm aiming for as close to old vanilla behavior as possible. Basically, I just want the Chinook to drop the crate like it used to. It has dropped maybe twice on my server since oil rigs were introduced. 

Because I am pretty sure it was hard coded by FP to drop on the big oil rig the majority of the time.

But, I've checked my oil rigs. There's already a hack crate there. It's always there. No one on my server is ready to take the oilrigs on yet. Kinda frustrating. If that's how it's supposed to operate, then I wish Facepunch would just say, "If you want it to drop elsewhere, loot the ones on the oil rigs."

In which case, to minimize the amount of times the crate will drop on the oil rig, I would suggest using 

"Prevent the game from handling chinook drops": true,​

to prevent the chinook from deciding on its own that the oil rig is the right place to drop.