I think the drop spawn timer starts as soon as the weapon is picked up, but it just won't respawn until it's dropped. So, if the rifle has a 3 minute respawn time, the timer will start as soon as you pick it up. If you drop the rifle after a minute, it would respawn as usual. But, if you don't drop it for 5 minutes, it would be forced to wait until you drop it to respawn.... I think...