It depends a great deal on what problems there are. Some problems will cause the Check Engine Light to turn on right away, others take some time. So depending on the problem, the light may turn on, on the way to the inspection station. In any case, the OBD will show that the battery was disconnected within the past 50 starts or so.
2005 Dodge Grand Caravan SXT, 129K mi.
Former owner of:
1988 Dodge Caravan SE, 2.5L I4 (1988-1995, 99K mi); 1995 Plymouth Grand Voyager SE "Rallye", 3.3L (1995-2004, 169K mi); 2003 Grand Caravan Sport, 3.8L, (2004-2008, 106K mi), 2008 Nissan Quest, (2008-2010, 25K mi)
2008 Lexus RX400h (Dark Gray), 112K mi; 2005 Hyundai Elantra GT (Blue), 89K mi