Hi Craig,
Thanks for getting in touch!
It is quite possible it will meet your needs.
WooCommerce itself supports a number of payment models (including manual options, where payment isn’t actually taken at point of ordering) and of course you can use WooCommerce Tickets to release free tickets – even if you actually accept registration payments by some other avenue.
Why not take a look at our New User Primer – that may give you a more complete taste of just what you can do and how flexible a solution WooCommerce Tickets is 🙂