By using a Deku Stick to perform the Forest Escape trick, it is possible to leave Kokiri Forest without the Kokiri Sword. Although you can become an adult without collecting it, you still cannot collect the sword as an adult however. This is because as an adult, it is assumed that you have already grabbed the Kokiri Sword from it's chest, so they remove the chest from the map as an adult. This is because the chest is extraneous. Adult Link can't fit through the crawlspace, so developers would assume that it will never be loaded or seen, and was therefore unnecessary to add to the map, since Adult Link and Child Link maps are different.
Bottle Adventure Edit
This is the only method which can be used to get a Kokiri Sword as an adult. Utilizing Bottle Adventure, you can put the Kokiri Sword onto the B Button. It looks like the Master Sword, but has the range and damage output of the Kokiri Sword. The Kokiri Sword has a decimal value of 59, so you need to use something other than an item quantity to do the trick (such as the Goron Mask or Zora Mask).