You can host Google Apps on your own domain, like s.archer@isis.org, but you can't register for a G+ account using that email address. You can only use gmail addresses, and not everyone uses or wants to use a gmail address as their primary account.
I actually set up another Google profile using an email account managed by Apps, and this works fine for me. But it's not the solution I want since you have to switch users whenever you want to use Plus.
It's advantageous to have them on separate accounts in case you are arbitrarily banned from Google Plus. This way it has no chance of affecting your other services. It would devastate me if I lost my main email.
Although it's unclear that Archer is set in the modern day and would have access to Google.
<< The characters wear 1960s clothing and hair styles and several episodes feature references to the Soviet Union as a current nation (the episode "Movie Star" hinges on the assassination of "the new Soviet Premier"). The technological sophistication within the series varies, with characters using computers that are dated i.e. reel-to-reel mainframe systems, dot-matrix printers and punchcards, yet also use cell phones, GPS devices, laser gunsights, and modern day insults (such as "suck it", "screw you", and "douche bag"). Adam Reed was asked about the conflicting style, and concluded, "I just think it's ill-defined." >>
Google offers a service called Google Apps. With this service, you can use a branded subset of their products at a non-Google domain. For example, you could use Gmail with a bob@mycompany.com address.
Because Google Apps is largely targeted at business/enterprise customers, it takes a while for some new updates and products to make their way into it; presumably the lag time is so that the the paid product can be kept as stable as possible.