It is definitely possible. My iphone 5 was hacked to the point they replaced it in Aug. and now appears to be hacked again. Naysayers please know - anything can be hacked. It was only a matter of time before hackers targeted iOS with the same tenacity they have targeted Windows OS for decades.
What happens on my phone this time is apps are opened I didn't open and Safari searches are initiated I did not initiate.
This was how it began in August, but escalated to phone calls made to people in my contact list, emails sent out to folks I don't even know, texts sent that I didn't initiate.
I even had Youtube begin and a live feed of a golf tournament start up while I was at work with the phone on the charger - not touching it.
They only replaced it at the Apple store when I showed them proof of stuff being sent out in the middle of the night when I wasn't on it and when it opened an App on its own while they were looking at it.
I work in IT and security is crucial to me. I have the phone pretty well locked down and it still happens.
So yes, it is possible. Next - what is Apple doing about it?