Hello,
Thanks for the interest in our Plugins. I can help answer your questions.
WooCommerce Tickets does create a product to sell the tickets, but as far as WooCommerce is concerned it is just a virtual product.
We do not modify the checkout process so the Gift Certificate plugin should work, but I cannot say for sure. We do offer a 30 day refund window so if it turns out there is a conflict we can always go that route.
Also, the ticket products by default does not show on the Shop page, but if you would like to you can edit it and change the Catalog Visibility.
Let me know if you have any follow up questions.
Thanks