Short answer - YES!
Quality also means matching the materials to the flies you will tie. Many lesser quality and priced materials handle and look better depending on their use. Quality dry fly neck and saddle hackle in almost always makes poor wet fly collars and streamer wings, respectively. Dubbing materials also need to match the type of fly tied, i.e. dubbing with a lot of guard hairs or a wiry synthetic make poor dry flies but good nymphs or streamers. Hairs need to match use. Some materials just look better (to us) and/or handle better, i.e. natural jungle cock, wood duck, etc.
I meant to add something fairly important to your question, "Do better tying materials make better flys?" Better materials make YOU a better fly tier.
Allan