I overfunded my HSA in 2019 and have spent most of the money on qualifying medical expenses. Does this count as a withdraw and allow me to avoid the 6% tax?

No, unfortunately, it does not.

To avoid the 6 percent penalty you need to remove the excess from your account and not take any of the excesses as a deduction against income. Alternatively, you can leave the excess in the account, pay the 6 percent and adjust your payments into the account for 2020 so that the excess is applied there. In both cases, you need to contact the administrator of your HSA bank account and have them fix it. 

"You may withdraw some or all of the excess contributions and not pay the excise tax on the amount withdrawn if you meet the following conditions.

1) You withdraw the excess contributions by the due date, including extensions, of your tax return for the year the contributions were made.

 2) You withdraw any income earned on the withdrawn contributions and include the earnings in “Other income” on your tax return for the year you withdraw the contributions and earnings."