Typically all power when starting the car is diverted to the starter motor. That means there's a momentary lapse of power to the cigarette lighter until the car starts, at which point power to the charger/BB is restored.
As for surges, they are normally created by the load itself, in this case, the BB. I would be surprised if the BB would create any kind of a surge because of a lapse in power.
I've forgotten to unplug my laptop a few times when starting the car. It's probably okay to do, but I try to avoid doing so just to be on the safe side. (I've heard that electronics might be sensitive to power fluctuations.)
For me, I may plug in a charger before I start my truck but I only connect my Berry, GPS, etc. after it's running, not sure if any damage would actually occur, just kind of a habit thing in my case. I have friends who constantly have chargers plugged in & the first thing they do is hook up their phones & then start their cars & they don't seem to have a problem, but like I said, it just may a case of preferace.
I would feel safer if the Lighter Plug had a surge suppressor. The 5.v converter in the charger plug would take the hit before the device. That failure could cause 12.v to hit the device POOF
