Yes, it is still possible to obtain plates in Sinnoh Underground after getting national Pokedex. It doesn't matter if you have already obtained the plates once outside of Underground in Sinnoh, according to Bulbapedia article here.
In Diamond, Pearl, and Platinum, the 16 Plates are spread far and wide across Sinnoh, and an additional copy of each Plate can also be dug up in the Underground.
However, according to Serebii, all the plates are very rarely found. As such, it could be that you haven't searched for them enough. Also, when you get the National Dex, some new items spawn, meaning that the plates could have their chance more less.
After obtaining the National Pokédex, however, the game will also yield Helix Fossils, Dome Fossils, Old Ambers, Root Fossils, and Claw Fossils. A number of items that were found rarely prior to obtaining the National Pokédex can also be found more easily now, such as the Evolution stones.
It seems that the plates aren't of these items which are found easily. Thus, if your game works fine, you may haven't searched enough to find plates. In that case, if you're not searching for additional plates, you can find some of them scattered around Sinnoh. This guide will help: http://www.psypokes.com/dp/plates.php
However, Draco Plate, Flame Plate, Insect Plate, Iron Plate, Meadow Plate, Sky Plate, Stone Plate, Toxic Plate and Zap Plate require the Dowsing Machine if you don't search for them in Underground.
Hope this helps!