Pip,
Buddy, go for it. I interned at Alaska Airlines over the summer of 2004. It was great, I got my letter stating that they will review my application when I get their mins. My log book also has 3.5 hours of 737-700 time and 2.5 of MD80. There are no negatives to the internship.
One word of advice, give it your all. 2 of the 12 of us got fired. Think about it, getting fired from a non-paid internship is hard, and could be career ending. Good luck.