If I get my iPhone 6 replaced at Apple store...

[Macbook14in]

Because of wifi connectivity issues, Apple would need to replace my phone with another phone. I know that this replacement phone is likely to be refurbished, but does it have any battery cycle count?

 

[hockeyman94]

The battery will be new not refurbished

 

[iDuel]

The battery inside of the refurbished device should be new. If anything, there will be a few cycles on the battery probably done when the phone went through QA testing.

 

[T5BRICK]

I know that this replacement phone is likely to be refurbished, but does it have any battery cycle count?

I've seen them with up to 10 cycles. Why does it matter? Anything you get will likely have a lower cycle count than your current phone. Plus it should actually work correctly.

 

[eyoungren]

Because of wifi connectivity issues, Apple would need to replace my phone with another phone. I know that this replacement phone is likely to be refurbished, but does it have any battery cycle count?

Remanufactured. Not refurbished.

New case.
New battery.
Any failed parts replaced.
Tested strenuously.
No difference between new.

No need to worry.