To use the WordPress Woocommerce quick edit to bulk publish draft products, first login to the backend and go to All Products and then sort by Drafts:
Choose as many items on the page as you want to publish:
If you want to see more products per screen, go to the screen options and change the number (200 might be really slow to load, 100 products is probably ideal):
After you have chosen all of the draft products on the page that you want to publish, change the Bulk Actions menu to Edit and click Apply to bulk edit the products you have selected:
Change the draft product(s) Status to Published and then click Update to publish the products on the current screen:
Go to the next screen using the navigation buttons and then repeat the process:
