Will apple replace my iPhone even though its customized?

So I got an iPhone off of eBay a few month ago and of course it has some problems like the home button not working properly, the speakers don't work, the promoxity sensor doesn't function, etc. And it wasn't abused or neglected or anything like that.
I'm not under warranty so I'm aware of the 149 dollar fee to replace it. But will they let me do that still even though there's a customized pink backing on it?

You bought a used phone, I wouldn't expect them to replace anything free anyways. Why would they?