I don’t know that this has ever been studied. That may be because there are many factors involved in “seeing some decent results”, the least of which, may be the order of the exercises. However, if you frame it in the context of whether the biceps or the triceps needs more improvement, or, whether your goal is big arms, then, order may make a difference.
For example, if your goal is big arms, you should look at training triceps first since they make up about two-thirds of your arm mass. Training them early on in your routine will allow you to attack the muscle with more energy and intensity. If, however, your biceps are the weak link, training them first should help. In either scenario, other individual factors (nutrition, genetics, commitment, etc.) are involved that will combine to form the basis for any potential results you receive.
The most important factor, in my opinion, is variety. Switching up your training (ie. alternating the order occasionally) affords you the opportunity to develop a more balanced physique. So, to answer your question, the order will matter only if you think it does.