Open Directory and "Local" Logins
Are both scenarios possible? Yes, the local node doesn't go away after domain binding. The order in which the Mac looks at bound directory nodes for user accounts is shown graphically in Directory Utility, which can be found in /System/Library/CoreServices as of 10.6+.  You'll also notice that even if you set OD to be searched before the default/local node, if the directory is not available(or not cached) you'll login to the local spandex instead of OD's.