I've heard this can be done on some ships, but not during peak times. One maitre d' on a smaller NCL ship told me that those wishing to reserve a table or waiter will have to dine before a certain time, say 5:45, or after a certain time, such as 8:30. This will vary from ship to ship, so check with the maitre d' when you board. I'm not promising it can be done, as it is ultimately up to the head maitre d'.
To add, the more in your party, lets' say over six, the more likely you'll be able to reserve a table during "peak" dinner times. But you will be able to reserve a table if you wish, but not always at the time you wish.
The vast number of alternative dining venues on Norwegian Spirit also works to your favor should you wish to dine in the main dining room. Still, check with the maitre d'. Enjoy your cruise!