A wizard can have buttons or links to help users enter correct input to the wizard's controls (e.g., a Browse button for a file name, or help links for additional documentation). It also might make sense in certain special cases to have a command link or button in a wizard to allow user to take one or another branch in the task flow. However, in keeping with the philosophy and application of a wizard, the branching choice itself should generally be separate page which clearly explains the alternatives. Windows User Experience guidelines recommend that you "put no more than one user decision on a single wizard page." If you don't need to explain each step, maybe you don't need a wizard.
But all that doesn't apply in your case, because it looks like users should always click Authorize -it's not a branch.
Efficiency of Alternative 1 = Alternative 2
I assume the alternative design is no Authorize button, but instead a Next button which executes the authorization check, resulting usually in another wizard page (Step 3) saying the URL is authorized, and the user then clicks the Done button. Your design may reduce the number of pages, but it doesn’t reduce the number of steps from the users’ perspective. Either way the user must (1) Enter a URL, (2) Click Authorize/Next, (3) Click Done. The amount of user effort is the same. Assuming pages load very quickly (and they should), the normative time to completion is also the same.
Your design in the meantime could be potentially confusing. What happens if the users selects Done before Authorize? Does the URL not authorize the URL (i.e., it’s Cancel, not Done), or does it attempt to authorize the URL without checking rights first? And if there’s no error message, does that mean the authorization was successful? Or could it have tried and failed silently due to insufficient rights? Whatever you decide the behavior is, how does the user know what you selected?
According to your user research, do users generally believe they have the rights to authorize the domains in questions? Or are they entering any old URL hoping they might have the rights? I’m guessing the former is true. If so, to improve the efficiency of the design, have no separate Authorize button. Make the Done button perform the rights check and complete everything else in the task in one step all behind the scenes, and then exit the wizard. The whole rationale for the "wizard" metaphor is that is does things automagically. There is no final “your domain has been authorized” page.
If the user clicks Done and the wizard exits, then the user will assume the wizard did what is was purported to do and authorized the domain. A separate “authorization successful” step does not provide enough information to justify its existence if the user is expecting that they have the rights. It’s too much like a “congratulations” page, which the Windows 7 User Experience Interaction Guidelines (page 16) advises not to include in a wizard. If the app finds the user does not have the rights, then stay on the URL page, display error text explaining the issue, and allow the user to correct the URL (which most likely had a simple typo).