In general, assuming this is a yeast-based dough, this is called retarding the dough, and if your dough is well-wrapped it should work out just fine. Beyond the convenience, there is actually one advantage to this method: the flavor of the dough tends to become more complex with the slow fermentation that the refrigerator will effect. Generally, it's best to refrigerate after you're confident the dough has a good active yeast culture, so I would recommend letting it rise a bit before stuffing.
The main caveat is that, for best results, you'll want the yeast to become active again before baking, which you'll need to balance with the total time that the meat might be in the danger zone for bacterial growth.
I usually find an hour in a warm room to be sufficient, but if it's cold weather or you keep your room cooler than 70F, you might be flirting with too much time in the danger zone. My oven happens to have a rapid-proofing feature and I find I can get the same effect by proofing for 25-30 minutes, then a more gentle rise while the oven preheats.
If you're using something other than a yeast dough, such as a pie dough, puff pastry or empanada style dough, then overnight refrigeration has no such complications.
Do keep in mind that regardless of what kind of pastry you're making, you don't want the raw pastries to touch each other, as they'll tend to stick together.