In short, no.
The value that your queue variable contains is a reference to the queue. This value won't change unless you reassign the queue like myQueue = otherQueue;
If all you are doing afer you create the queue is putting things in and taking things out then it doesn't matter if a thread has a cached value because the value (the reference to the queue) never changes.
It's good practice to make all variables final unless you need it to not be final.