Does BQE CORE track the statements or invoices emailed out?

No. There is no tracking of emails sent out of BQE CORE to your clients. However, if you want to keep track of the statements or invoices emailed to your clients, you can set your own email address as the CC or BCC recipient in the Settings > Company > Email Settings screen. The same can be done in the User Settings > Email Settings screen. This way, you will receive a copy of every email sent out of CORE. Check CORE Help Center for more details.