EVOO has a lower smoke point than most deep fryer standard settings, which are often 350-375. For high temperature deep frying, you want something like peanut oil or grapeseed oil (although the latter is more expensive).You can deep fry with olive oil, even EVOO. I wouldn't, simply because EVOO is more expensive than other frying oils, but you can fry with it. Just don't put your fryer past 380° (I don't know why you would anyways) and you'll be good.
Also EVOO emits an acrid smoke when it hits smoke point and the flavor goes off. Supposedly it also polymerizes and might generate carcinogenic compounds. Its flavor is wasted on deep frying, although it's perfectly good for medium/medium-high pan frying.
I'd usually use it for grilling sandwiches or in sauces or to pan fry lightly breaded fish or white meat but that's just preference.