Beef broth vs. beef stock
Yes, certainly, but it won't do as much good as you might expect. It takes a surprisingly large amount of meat to add significant beef flavor to beef stock.

If you want to go ahead, be sure to brown the extra meat, to get maximum umami flavor out of it. (You will want to brown the bones, too; I'd roast them in the oven.) Another way to add extra beef flavor is to throw in some ground beef, which has the nice benefit of giving up its flavor quickly.

But it might be better to throw it all in a gallon ziplock and stick it in the freezer. Keep accumulating bones, then make a potful of stock all at once. (You can keep them for months, or even longer. The biggest worry of freezing meat is freezer burn, which isn't a problem if you're just making stock.)