The "Service Engine Soon" or "Check Engine" light has to do with anything emissions related (exhaust, ignition, fuel evap, vacuum leaks, etc). The car constantly checks itself. If it detects a fault, and depending upon the severity and number of occurences, will set a light and log the event in the computer's memory. If the fault goes away for a while, the light will turn itself off after a number of run cycles, but the fault will still be stored in the computer with the number of occurences and at what time (running hours) they occurred.
The Oil Service/Inspection lights are based upon an algorithim BMW came up with based upon fuel injector cycles and duty (amongst other parameters). I guess the only correlation could be if your Inspection II has been overdue by months in severe driving conditions, then the poor running conditions (old oil, bad plugs...) could set a check engine light.