If I connect the Blue Snowball Microphone to an iPhone with a Lightning to USB Cable, will it record?

99% sure no

usb mics are made for computers and require a driver

not a driver ios would support unless the maker had an app which could use their usb device

The manufactuer would be a better source for that information, I would think.

the headset connector have 3 rings the middle on is mic in you could camabalize a cable and connect a mic directly into the headset

mind you make sure the mic signal you put in is not too powerful vs. the mic in headsets or you could blow something