Yes, in Alpha Protocol you wake up to find you got the job but your employer doesn't want you to know where the office is. I would advise against taking a job anyplace where the commute to and from work involves sedation.
The "you wake up to calamity" is a really common videogame trope, although for some reason I can't find it on TV Tropes. It's always the same: You wake up, the place is in peril, alarms are going off, and you're in your underpants.
It's a natural starting point for a game. There's excitement and alleged danger to spice up what would otherwise be a dull tutorial. You're in your underwear so that the game can gradually equip you with armor, weapons, and gadgets without overwhelming you. And the fact that you were sleeping gives a reason for why you have no idea what's going on and why everyone has to explain everything to you.
Other notable instances:
KOTOR II: you wake up in a healing pod on the soon-to-explode Pegasus mining facility.
System Shock: You awaken from a healing coma after having a cybernetic implant installed, only to find that the computer has gone crazy and is killing everyone on the space station.
System Shock 2: Same thing, except on a spaceship.
Neverwinter Nights 2: You wake up, your dad sends you to the tutorial harvest fair. Not exactly a calamity, but then that night your friend wakes you up because the village is under attack.
If I missed any I'm sure you'll let me know.