I have only heard of a few forums doing giveaways, it will attract the attention of some people who want to get the item, but I don't know if those people will revisit or not.
Giveaways can be very beneficial for your site. Feel free to make an official announcement in the What's Going On board. It would also help catch people's attention on what it is exactly that you're giving away and how can people win. 😉
I feel the only way I would do a giveaway unless I had a well established community with a good amount of active members. It would be a way to give back to the community.
Just like with the ill concept of putting together contests, giving anything away is a desperate move to attract new members. I'm willing to bet that if you manage to get anyone in, they either would just join to get something from you or only last less than a month or two.
Giveaways do sometimes help your forums though they can do just as much harm as they can do good. Sometimes giveaways are not beneficial so if your doing one ensure it's done correctly 😛