Yes, you can download a list of both unreconciled & reconciled records in Jaz.

You can export a list for all time, or choose a custom date range.

The final export will show a list of all unreconciled transaction records that have the bank account as its payment account in the Unreconciled Records Tab.

You can also view unreconciled bank statement lines under the Bank Statement Lines tab.

You can see a list of reconciled bank statement lines via the Bank Statement Lines of the Reconciliation Report.

Refer to Q1. Can I export a list of unreconciled records? for more information on using and downloading the reconciliation report.