I'd like to combine Item Rarity (passive blue) with my AoE Rain of Arrows (active green). Of course I can socket these gems the way I want, but will the Rain of Arrows benefit of the Item Rarity's boost ?
"Yes", you can. That's why different colors tend to be linked at all.
The only thing that wont work is bad mechanics logic (Multiple Projectiles/Fork and Glacial Hammer for example, do not work together that well).