Can the Splunk-driven reporting process send a report via email with the results based upon the specific criteria?
I don't understand what you mean by "specific criteria". But you can schedule a search to run and send its results via email. You can also schedule an alert to run and search and then send the email only if certain conditions are met.
Here is the documentation on setting up an alert; or just click Create->Alert.
A scheduled search can be created in 4.3 by clicking Create -> Scheduled Search.