Are there any benefits in refrigerating stock before using it? I'm at the tail end of cooking a chicken stock and was planning to use a small portion of it in a marsala sauce later in the evening. Every chicken stock recipe I've read says to let the stock cool then refrigerate. To my understanding, this is not only to preserve the stock but also to allow it to become gelatinous? Will I lose out on any flavor by going directly from the pot and into the pan?
Any gelatin in your stock will be there whether it is warm or cold.  It's just that gelatin solidifies when it cools...it will melt out when you warm it again, leaving you where you are now.  You can go straight to your sauce, your stock is probably as flavorful as it will be when you are finished cooking it.  Cooling prior to refrigeration is to prevent the potential warming of other items in your refrigerator, and has little to do with the stock itself.