Yes the check engine light illuminates every time you turn on your car to show that it works. It then turns off with all the other lights.

1) have them fix your check engine light
2) get the DTC code(s) that are set. Write the numbers down, I can't tell you how many times ppl f the #'s up. (goto autozone or murrays, they read them for you)
3) You'll fail emmision just because a DTC is set.
4) If your super lucky your dealer will fix all these problems for you. (doubt it though, they are already scamming you)

Dealers do this all the time, they "clear" any engine codes/SRS and sell a used car. The codes don't get set untill it goes thru a few normal drive cycles. A 5 min test drive doesn't count.

So.. you bought the car and tough, you should have got it checked out before hand. Dealers are doing this even on "Pre-Owned Certified Vehicles" I should know I bought an Acura that did the exact same thing.

Good Luck, you'll need it.