That's a tough question. The answer is yes. You can add the ram and see if they work. There is a reasonable chance they won't work. The reason being is that although the two sets of DIMMS might have the same speed and latency, it's often the sub timings that are different. Also, voltage plays a part too. The best solution is to only have a matched kit in either 2 or 4 slots. (Sometimes six or more for triple and quad channel motherboards)
You could get them to work just fine, but they may not work together. However, if you do get them and they don't work, at least you have a new 16gb (2 x 8) matched kit, that should work just fine by itself. 16gb is plenty for a gaming system.
I'd suggest just getting the new matched kit, and selling the current set to offset the cost.
edit: it's always a good idea to buy ram on the QVL for your motherboard. Please list your PC specs, the ram you have and the ram you have chosen to add, and we can better advise.