[eschwartz]

Ummmm...

The jailbreak works fine regardless of Special Offers.

Now, the Screensavers hack doesn't work with Special Offers enabled (obviously) but that is just one of our aftermarket addons -- the ones you are interested in have nothing to do with Special Offers.

...

We have had conflicting reports about using the initial factory images. A small minority of users have had issues, regarding passcode-enabled and Special Offers Kindles.

I doubt it though, since the real cause seems to have been a specific combination of firmware + device model and we have stopped distributing the faulty firmware image.
And there is nothing about the jailbreak that is incompatible with Special Offers. We just cannot entirely predict the effects of Amazon's initial factory image.

(Amazon uses them in the factory, obviously. But they assuredly don't bother to test them with passcode-enabled or Special Offers devices, since they aren't meant for consumer use. And untested things can have unpredictable behavior...)