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No because the vector can also change in magnitude. Even if the spiral was perfectly aligned to impact the perfect center of the Earth we could change the magnitude of the object by nuking either pole to either slow it down or speed it up. Enough energy on any pole could make it miss regardless of the orientation.

If you can make the asteroid cross Earth's orbit 430 seconds sooner or later that's an Earth diameter.

Two approaches to getting that number...

https://www.wolframalpha.com/input?i=diameter+of+earth+%2F+%...

https://www.wolframalpha.com/input?i=%28430+seconds+*+earth+...

Granted, you'd probably like more than a diameter... but we're talking about it getting there a few minutes faster and it would be a miss.

Perfectly chaotic rotation might be worse. If it was a spiral then you could hit it at a pole. I think most things rotate about a semi-fixed axis (not totally fixed, often propagating over time)