Yes, ApprovalMax supports pulling existing Bills from QuickBooks Online without going through the appropriate approval workflow in ApprovalMax.
Besides, you can create your Bills directly in ApprovalMax, run them through the predefined approval workflow and then push the approved Bills to QuickBooks Online. This works the same way as the creation of Purchase Orders. For further details, please refer to our article: How does the Bill Creation and Approval workflow for QuickBooks Online work.