It's not necessarily the same. Ribbonstone has a point in that military brass is typically harder and springier, so it may not come out of the chamber with the same exterior volume as the softer commercial counterpart. And Fguffy's point about the difference in some brass at the rim is a reminder that cases have tolerances. +0" and -0.008" in diameter of the head, for example, and the head does not expand with the rest of the case on firing. That tolerance can result in different external
volume, all appearances to the contrary, and that would mess up the brass density-based calculation.
The way to tell is to take something like a .45-120 case or any other container that will hold a .223 case completely and won't exceed the capacity of your scale when it is full of water. Fill it about half or two thirds of the way with water. Set it on the scale in a powder pan or a small paper cup to catch overflow and note the total weight. Plug the mouth of your .223 case with clay and level it. Tie a loop of fine wire around the extractor groove and bend it so the case dangles straight up and down. Put a mark on the wire with a Sharpie which is the depth the wire will be submerged to. It must be close enough to the case so submerging to that mark will not let the .223 case touch the bottom of the container. Submerge the .223 case to the mark on the wire. If the case overflows into the pan or cup, that's OK, it won't affect the measurement. What you need to do is get the new weight with the case submerged but not touching the container. The additional weight shown on the scale under that condition will be the weight of the water displaced by the plugged .223 case and its wire. That weight increas will reflect the number of cubic centimeters of volume the exterior of the case has, plus that of the portion of the wire that is submerged. The wire doesn't matter because you are looking for a difference in displacement, not an accurate absolute volume. Repeat with the other case. The difference in the the two volume readings will tell the tale as far as exterior dimensions go.
You will be looking for a difference of just about 1.2 grains in the results for the two cases. That should register just fine on a powder scale. If you want to improve the accuracy of the measurement, you'll need to know the temperature of the water and adjust the result for its density at that temperature. There is a water density calculator here