Thanks for your enquiry concerning BackupBuddy.
Certainly BackupBuddy is a site orientated backup/restore/migrate solution and as such when a site is restored/migrated the it replaces the existing site.
For the particular requirement that you describe a common workflow is to use the WordPress Export/Import tools to keep the development site content synchronized with the live site (which is helpful in any case if the development takes a while as you want to make sure that new content is compatible with whatever updates are being made) and then when the time comes to replace the live site then it is temporarily taken down for maintenance (thus preventing updates temporarily), a final sync made and then the development site is migrated over to replace the live site and you are up and running.
Alternatively, for the specific case that you describe where it is only the theme that you are modifying, then you could simply take the course of uploading the new theme version to your live site and activating it - of course as you will probably require to do additional theme configuration and there may be some minor associated changes in other aspects of the site you may still wish to take the live site offline temporarily for maintenance whilst this is all being configured - but using BackupBuddy you can set up a test version of the live site and do a run through of the process so it will run smoothly when you do the live site update.
I hope this has provided you with the information that you require, please feel free to ask for any clarification or additional questions as necessary, thanks.