No. We get the dreaded Kernel Panic instead. Granted, they are far more rare than BSOD's ever have been, but I'm told they do happen. (Just not to me) :-)
Full Disclosure: I was woken up in the middle of the night about 6 weeks ago. It was my HP printer vocalizing "RED ALERT! RED ALERT" with a siren-type sound howling as well. and apparently there was something akin to a general protection fault with the driver.
Never did go back to sleep, either -- sounded too viscerally like a fire alarm.