yes! Depends on where you want to go and what you want to do. The best thing to do is pick a hospital and ask them - if they want to take you they'll let you know if there is a formal application process to go through.
For example, a friend of mine wanted to do a couple of electives in Tasmania, but was told by the med school there that they weren't offering any electives - so he wrote to specific departments within the hospital he was interested in - and ended up with several positive replies.
If you have the time to search, putting a name to your letter helps (i.e. find out who the clinical director of the unit is and write to them etc)