No MMU.

A1000 has... something. The WORM (write once read many), RAM used for the kickstart, which is latched as read-only after the kickstart has been loaded from floppy by the bootstrap ROM.

No, there's no MMU.

Well, apparently if your CPU has one (030+) you can use something like Enforcer (http://www.sinz.org/Michael.Sinz/Enforcer/). I’ve yet to try it.