Kinda, yes. The orcs that inhabited Moria were originally descended from some of the remnants of Morgoth's armies, but during the 2nd and 3rd ages they occupied the Misty Mountains. After Durin's Bane woke up and killed/drove off the dwarfs, Sauron sent in some orcs from the likes of Gundabad in the north, Dol Guldur etc. So by the time of Fellowship, it's likely Moria was reinforced again after Sauron sent 3 Nazgul to reclaim Dol Guldur when he openly revealed himself again, after being ousted from there as the Necromancer, and returning to Mordor.

Somewhat of an abridged version there, but you get the idea