No. There are times for dried herbs, but this isn't one of them. The pasta is actually quite light and wonderful because it has fresh lemon and fresh parsley.
Dried herbs are really good for when you are stewing something for a long time and it has a chance to re-hydrate and give off it's flavor. The parsley in aglio e olio is on the heat for MAYBE a 2 minutes while the pasta water forms a better sauce, and it's such a low heat that dried herbs wouldn't do much in terms of flavor
Also, parsley is fairly cheap, and the bits you don't use (stems) can be tossed into the freezer along with other kitchen scraps and dumped into a stock later
Hey /u/OliverBabish, herbs and spices would actually be a good basics topic ;)
And yes will be doing a spices/herbs essentials Basics episode soon!