Can I query Cadence contact records to identify records that only contain a mobile number?

Currently, there is not a way to query this information. The best way to generate a list showing records that only contain a mobile number would be to export all contact data under "Team Name" > Reporting > Exports > Contact Data.

Note: Only Admin users can export contact data.

Additionally, utilizing  Notifications can help manage instances when an unknown/"cold contact" number sends a text to a Cadence user, or a Cadence user manually adds a contact to the platform.