Almost immediately. I just happened to review today's drop list and I put together a list of approx 50 names I was interested in. At approx 3pm (Eastern US, about 30 minutes to 1 hour after the drop) I tried to register all of them through a bulk registration. 46 came back unavailable and 4 were available for registration.
I'm pretty sure that all of them had dropped by that time so the 46 that were unavailable were either picked up by drop services or hand reg'd by others that tried before I did.
The .com drop time is supposed to be 2pm Eastern USA time. I've registered .com's as early as 2:03pm on the day they dropped. They don't all drop at 2pm. I believe they are dropped in batches between 2pm and 3pm. Something that is unavailable at 2:10pm might be availabe at 2:45pm.