The short answer is 'No'. QuickBooks's parent company Intuit does not allow API access for cloud-based products like Gazelle to build 3rd party integrations to their offline product 'QuickBooks Desktop'. Additionally, their online product 'QuickBooks Self-Employed' does not support API integrations and their online hosted 'QuickBooks Enterprise' products use a different API than QuickBooks Online. This means Gazelle's QuickBooks Online integration will not work with QuickBooks Desktop, QuickBooks Self-Employed, and QuickBooks Enterprise products.
What QuickBooks products does Gazelle sync with?
QuickBooks Online Essentials
QuickBooks Online Simple Start
QuickBooks Online Plus
QuickBooks Online Advanced
IMPORTANT NOTE: When migrating from QuickBooks Self-Employed to any of the QuickBooks Online family of products, Intuit does not make this transition smooth. When you upgrade your QuickBooks Self-Employed into QuickBooks Online (depending on your situation) it may be easier to close out your books in QuickBooks Self-Employed, transfer the account balances to QuickBooks Online, and do a fresh clean start in QuickBooks online. Consult your accountant to understand any impacts this change form QuickBooks Self-Employed to QuickBooks Online may have on your QuickBooks Self-Employed data.