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Well, yes, but no.
Without careful selection and culling of rejects, those birds that breed will eventually begin to water down the genetics within the breeding pool. In time, they will be begin reverting back to the very core of their genetic makeup and can wind up looking, behaving and performing nothing like the ones you started with.
Oh, this stuff wont be noticeable at first. If you are prone to a casual approach, you may not notice it for years. Then one day you'll look around and realize you see more dying this year than you recall, or fewer eggs being layed, or fewer chicks hatching out, or more "funny looking" chickens than previously, etc.
If "similar quality" is good enough for you, then I expect you'll do fine. If bettering your flock is of any importance, then you'll have to take steps to ensure that happens.