I lived in the USVI for a year and a half - island fever is definitely something to be concerned about. If the job has any travel, you should be ok though.
I definitely recommend the experience, even though the USVI was actually a horrible place (mainly due to the total seperation of races), but I believe the BVI is less polarized in that regard.
I would caution that the fantasy you might have that you're going to live in paradise is just that - a fantasy. You'll still have to work and pay the bills - it's not a vacation. So time-off is time-off - i.e. the weekends. But think of all the fun you can have there which you might pine for living in the cold city of Chicago? SCUBA, margarita's on the beach, sailing, wind-surfing, the water that is so clear you can see a grain of sand on your toe while standing to the neck in refreshing bliss.
Hurricanes aren't as bad as people think. Sure, your house might get the roof blown off, but it's much more rare than you would expect on an island. I survived 4 of them on St. Thomas - it's mainly some wind and a lot of rain. The tornado strikes are what take out the buildings.
How 'bout this - if you don't take the job - give 'em my number!
