Hi Jesse,
If you are using Excel Importer module By default logs will be captured here but not exactly all information like Number of records etc.
But you can able to achieve this in manual way, First think create one Audit Entity to capture all relevant details as per requirement. After the Java Call StartImportByTemplate, you can create Audit object along with File records count and date etc information.
Hope it helps,
Thanks & Regards,
Manikandan K