Of course it's possible, as evidenced by certain people doing it.
Yes for sure i think the iphone needs one for sure. here is one from a site i go to all the time
I initially always said the iphone should have a screen protector, but this last time around I opted not to have one at all because I am super careful with my phones and the last one that had a screen protector was just fine, no damage on the screen protector or anything. However, this one without a protector that I got in October of last year, I was out in the sun using it and then hit the power button to put it in standby like normal however when the screen went blank I caught a glimpse of a scratch with the sun hitting it just right and sure enough as I tilted the phone screen around there were a few scratches right in the middle of the screen, straight up and down where I always scroll webpages, contacts, etc. It's impossible to see under any other light other than sunlight, and even then the screen MUST be off too. I doubt it's a coincidence because that's the ONLY spot there are scratches. I keep my nails trimmed and have the softest girlish hands imaginable (I've been told by numerous people how amazed they are how soft my hands are. :-S ) but the phone screen still got scratched just with the regular friction of my thumb against the screen, so yes, I would say the iPhone needs a screen protector.
yeah they also have those smudge proof screen protectors now too that are pretty nice. so i definitely think one is necessary you never know when you might scratch up your screen. better to have it and not need it then need it and not have it i always say