I have On-Star in my 06 and have had it 3 yrs. I had to change the battery last year. Don't know if the previous owner had any problems but doubt it. It had 24k miles on it. It now has about 85k miles on it!
I like driving my Vette! I have not noticed a battery drain from the On-Star. But if you don't drive it much that might be an issue.