Yes, a free trial comes with each install.
Note: Installing Auto Convert to your production environment requires you to provide your credit card information. No charges are added until the trial period expires. To prevent charges from being applied to your credit card YOU must login to the AppExchange and Cancel your subscription. Go to appexchange.com > Login > Installations and Subscriptions > Auto Convert > Manage Subscription > Cancel
Installing Auto Convert Leads to your Sandbox does not require you to provide your credit card information.