not entirely correct johnny!
the coil works on a back emf, which is why you get a spark when the contact breaker opens. as the current in the primary dissapears, it induces a current in the secondary, and due to the number of windings, creates a high voltage. current is very low.
oh, an its ositive an negative, on dc, not live an neutral
not nit pickin, but the bad connections as you say wont help!
edit.
thinkin about it, you,ve pretty much just descibed an ignighter coil for the likes of jetwash burners or industrial fired boilers!