Hey there AdrianTO. Thanks for your note, and your interest. To answer your question here: yes, tickets you add as WooTickets within The Events Calendar are set up as products. They will not appear in the frontend cart by default, though.
I’m not sure about the element of adding the items to your cart, largely because that would be a WooCommerce function (our plugin just taps into WooCommerce and makes use of its code to sell tickets). I would bet that if you found a way to make this work for regular products using WooCommerce, though, there shouldn’t be any reason why it wouldn’t work for WooTickets. And if you bought and found it DIDN’T work in WooTickets (despite working fine in WooCommerce), we’d certainly be happy to give you a refund as desired.
Hope that helps. Please let me know if it didn’t, or if you have other questions. Cheers!