Anything is possible. Cheap power adapters often have poor isolation between mains voltage and the low voltage side that goes into your phone. If that shorts out, it will not only harm your phone it’ll also harm you if you’re holding it. Is that likely? Probably not.
I think the question you’re asking is does a cheap power adapter, give inferior quality current and shorten the life of the battery or circuits inside the phone. I’m not sure, but that would be interesting and could explain why some people have battery issues.
You don’t need to buy Apple branded but I would avoid going for the cheapest possible.
