No. If your paused request reaches the top of the queue and your suspension date has not arrived, then the request will not be filled for you. Your request will remain at the top of the list until your suspension date arrives and then it will be filled when the item is next checked in.
If you want to reactivate a paused request sooner than you had planned, put a check mark next to each request that you want to reactivate and click on “Manage Items” and “Resume holds.” Your request will no longer be paused.