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Generally not, especially if there has been no record of prior repairs.

Batteries are a funny thing where they're not really covered unless being shown as defective. Batteries degrade over time so apple will not replace a phone just because the battery will not hold a charge. At most they'll replace the battery for free
 
If it's relatively new, maybe. If not, forget it. Batteries are known to degrade over time, especially when not conditioned properly.
 
I dare say so..

So far I've been dealing with 'em.. Apple has been rather good when it comes to replacements etc...

Although... my experience is based on new (within 14 days from the purchase) items..
 
Use iPhone Regularly

For proper maintenance of a lithium-based battery, it’s important to keep the electrons in it moving occasionally. Be sure to go through at least one charge cycle per month (charging the battery to 100% and then completely running it down).
Let It Breathe

Charging your iPhone while in certain carrying cases may generate excess heat, which can affect battery capacity. If you notice that your iPhone gets hot when you charge it, take it out of its case first.
From Apple FAQ
 
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