No. It is now treated as an "indirect" start of play. This is a rule change that has happened in Aug 2012. It will now be a GK or CK (unless the goal keeper has touch it, on the way to the goal. So effectively you can not score an Own goal as well.
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Yes. A goal may be scored directly from a drop ball. A drop ball must touch the ground before any player may kick it.
Addendum: This is no longer true as of 2014/15 season. A goal may not be scored on the first touch from a drop ball.
New rules for 2012/13 now state that you can no longer score directly from a drop ball. A goal kick will now be awarded instead.