Good god yes!
And make sure you get insurance as well (an E111 doesn't cover everything) and read the small-print to see what it covers as often things like watersports and going off-road with a Jeep aren't included.
It might seem like there's no point and you'll be fine, but having had to call a doctor out in the middle of the night after some blood poisoning last year, I would thoroughly advise EVERYONE to do it.