Will restore from backup make your wifi greyed out again?

This is the same issue with upgrading to iOS 6.0.1 and my wifi greyed out after 2 weeks. I deleted files and restored it back but to no avail. Sent it back to my carrier and they replaced it with a brand new one. And this new one's OS is already 6.0.1. If I back up my phone from my computer, will it affect the wifi? I called Apple Support both local and US and they told me that it was a hardware issue and that it shouldn't affect the wifi even if I restore it.

I don't want to risk my phone again with a non working wifi and the inconvenience of sending it back. Did you guys had any issues about this as well? Did it affect your wifi? I am on unli data but I wanted my wifi to work as well. Thanks!