I expect it will pick up items on the ground that haven't been touched yet even if the goblin is summoned after they drop, but can't say for sure until I can try it out.
Yes, that's how it works. The goblin picks up any white items on the ground, regardless of when they dropped. I've thrown junk on the ground for it from my inventory before and it snatches them up.
I just did a real world test to confirm and it is so. Took ring off. Spawned an item in Battlefields. Put ring on. Goblin picked up item.
EDIT: Spoke too soon. I took the ring off and spawned a white item from Battlefields. Put it in my inventory. Went back to town. Summoned goblin. Threw item on ground. It wouldn't pick it up.
So there are some limitations. Not sure exactly what the step that breaks it is, though. Would need to test a little more.
EDIT 2: Did a little more testing. It's picking up the item that breaks it. So as long as you don't pickup the white item, it doesn't matter if the goblin is up when the item drops or not. You can go through and clear out an area, then put the ring on, but you can't pickup all the white items as you go, then dump them for the gob to pickup.