Ability to give away iOS application, usually for sale I am wondering if it's possible to do "mass giveaways" on the AppStore, without lowering, changing or otherwise changing the listed application.

Is it possible to distribute hundreds to, potentially, thousands of promo codes, legally, while still leaving the "normal" distribution channel of purchasing the app open?

An example of the above would be selling physical items in a store which have a bundled digital component available. Essentially you buy a product in a store, which comes "bundles with a free app" (BB and Android have already been dealt with, iOS is unclear). It would be nice to give the option to have a promo code in the box, that the user can then use to get the application for free. Is this possible?
No. Apple allows for only a very limited number of promo codes for the lifetime of an application (versions 1.0 - n.0). The exact number escapes me at the moment but somewhere around 100 comes to mind. You are allowed to have more beta testers, but that requires manual management of every user and isn't scalable should you need to go beyond your limit.

At the same time, there are pricing strategies you are free to implement, like free for the first 30 days, holiday and back-to-school sales, and the like.