Not necessarily. Let's say you have Department A and Department B. Let's say your Agent account only has access to Department A. Now, let's say a Ticket gets created under Department B and you (or your Team) are Assigned the Ticket. Since you are directly Assigned you will be able to interact with that Ticket even though you don't have access to the Department. Now, once you (or anyone else) Closes this Ticket the Assignment is Released (removed) and you will no longer have access to that Ticket (even in the Closed Queue). Now if a Ticket was created under Department A and you Close it, you should be able to see it in the Closed Queue.
With this being said you can enable an option for your Agent Account to have the ability to Search all Tickets even ones you don't have access to. You can only search them and will not be able to see them in queues, click to view them, or interact with them in any way. You can just see the basic data displayed (Number, Created Date, Subject, From, Priority, and Assignee).