Can I recover a deleted world?
A deleted file on your harddrive may be recovered using file recovery programs, given that there hasn't been written too much to the disk afterwards. However, there are no guarantees.
MAC has several alternatives, however I haven't tried them. EaseUS Data Recovery Wizard is one example.
Sidenote: For PC-users there's (for instance) Piriform's Recuva you could try to use.
If the key operator of the machine had the foresight to enable Time Machine, that could be used to recover the files.