Greg,
A science degree would help with the groundschool, however your course is highly relevant. Most airlines aren't simply considering your ability to fly, they're looking for future captains - knowledge of business management will be a real bonus when you come to apply. If you have ANY choice in your projects/thesis, do your best to relate them to the airline industry - valuable knowledge and the possibility of making contacts for the future. Spend some time brushing up on your physics and maths though, you'll need it for the apptitudes.