That circuit will not work. One simplification you can make when trying to understand circuits is to assume that power supply rails are fixed voltages. That's reasonable in your case. Notice that the voltage at these nodes are fixed:
If the voltage is fixed, it doesn't matter what else is connected there. The igniter and the 10k both see VBAT. They can't effect each other. It's like 2 people pulling on a sign post. They pull one way, you pull on another, but you have no effect on each other because the post is "fixed".
Luckily, you can easily fix this circuit by moving your voltage divider to the low side.
And of course we should check the current through the igniter. 8.4/15.1E3 = 0.56mA. That should be fine.
