Is the security indicator light supposed to blink when the car is shut off

Yes. This is normal.

If someone tries to break in to vehicle does security indicator light set off an alarm?

I'd say this is not normal, because my Wife's 2014 had an issue where the radio stayed on when she turned off the car and then that light blinked. I had her start the car go in reverse, then forward and park. That fixed the radio, but now that security light blinks every 2 secs when everything is shut off. Never did that before and we have owned it 6+ years.