The most straightforward answer is "no". As the Django Book says, the admin is for "Trusted users editing structured content," in this case the structured content being models arranged in hierarchies and configured through settings.py. More importantly, if your object doesn't completely duck-type to a models.Model complete with expected relationships, the admin will probably toss exceptions all over the place.
However, as the mantra goes, "It's just python." You can override any of the pages in admin. Just create your own templates in your project, and have them come first in the template search. Also, by inheriting admin/base.html, you maintain the look & feel of the administration project.
Write your administrative view and templates for this object, just like any others, but making sure to wrap the views in the is_staff decorator to ensure that the views are protected from access by unauthorized users. Put those in the application, perhaps in admin/views.py, with templates/admin/object_list.html and object_form.html.
Once you have appropriate administrative tools for these non-database objects, you can then provide access to them through the administration index page: You want to override admin/index.html, and provide additional project-specific items to the page as needed.
I have done exactly this to provide administrative access to third-party APIs that store our data, such as the ConstantContact email service, and it works pretty well.