I want to be able to provide the admin with a function so that they can email all registered users of the site.
Is there a native function or plugin that would make this possible?
Natively, there is no direct way to do this. It is possible, however, to easily create this functionality with a plugin...
Build an ElementCriteriaModel which will return a list of all users. Organize that data into a batch (or multiple batches) of recipient email addresses.
Use the EmailService API to generate an email to your selected recipients.
Depending on your specific plans, some other small "in between" steps may be required to suit your individual needs.