Is it possible to pick up a thrown glowstick in Terraria?

Solution 1:

As per the wiki:

The Glowstick is a light source that can be held or thrown, and works underwater, but can not be placed in a wall or floor like the Torch can (though the Sticky Glowstick will stick to surfaces they are thrown against). Glowsticks will emit light for a lengthy period of time after being thrown, and have a 1:3 chance to be recoverable after several minutes. The Glowstick can be bought from the Merchant, at night, for 20 Copper Coins. Glowsticks are also dropped by all Jellyfish, and can be found commonly in Pots and Chests.

So yes you can pick it back up, only if the Terraria gods feel you should. This info should be relevant as of 1.0.6