Yes — as long as you subscribe with the same email address you used for the trial. Your projects and events are stored against your email, not against the trial, so subscribing simply unlocks them again. Nothing is deleted when a trial expires either: an expired trial locks the premium features, but everything you saved stays exactly where it was, however long it sits there.
The one case to watch is buying under a different address — for example trialling with your own work email and then subscribing through a shared billing address. Sign in with the new address and you will see an empty designer, because as far as your saved work is concerned that is a different person. Nothing is lost; it is simply filed under the other email. Contact us and we will move the subscription’s seat onto your original address, and your projects reappear.