This question made me very curious, because I think it is a very interesting questioning and when I tried to look for information about this, there's basically none information about it, so I decided to contact Cipsoft support to clarify this doubt.
- Are the items in the reward chest transferred too? No
- Is it necessary to collect rewards before transferring worlds? Yes
Cipsoft tech support answered:
The rewards in the Adventurer's Guild chest are locally stored on the current game world of the character. Therefore the rewards can no longer be collected after the character transferred to another game world. If you have the intention to use a Character World Transfer, you should definitely make sure that the chest is empty.