If you are talking about Q2 on the timer board then No it does not work that way. Define "on" state and "off state"

IF a NPN transistor is "on" then the transistor is fully saturated and the Collector and the Emitter are connected. With that being said if the emitter and the collector are connected this creates a low signal , which causes the .1 uf cap( in hv board) to discharge to the gate of the SCR, thus causing the 400v .47 cap to discharge through the ignition coil.

With a 680 ohm resistor feeding one side of a .1uf cap and a 220 ohm resistor on the other leg of the cap. the cap charges. a low going pulse at the 680 resistor/cap junction is what causes the 1.cap to discharge. There is no way that the SCR is "held on for too long".