The answer is no.
Deposit field on Invoice is below the total field. It does not compute sales tax on deposit (acts more like pre-payment) field in QBO. If you run the Sales Tax Liability report from the Sales Tax Center (View sales tax liability report under Related Tasks at the far right side). Just click the tax amount. It will take you to the Transaction Report. You can run this report on a cash basis, you will not see sales tax amount on that deposit or the taxable amount on that invoice total. Of course, on an accrual basis, you will see sales tax amount on the whole taxable sales invoice amount.
In this example, refer to invoice #15-00334 with $100 deposit. No tax amount on a cash basis. Only tax amount on an accrual basis. That is the way it’s supposed to be.