Of course you can do that, but I recommend getting PS way in advance as those choice times book up fast. Also the problem is that diners who have window seats tend to linger for the same reason as you...to see the fireworks.
If you were only having dessert and coffee, it may be difficult to justify sitting there for an hour and a half which is when we usually schedule our PS for the fireworks.
If you can't get a window seat, you can always view the fireworks from the observation deck.