After reading this question, I asked myself the following questions:
Do answer votes affect question votes?
Do question votes affect answer votes?
You seem to indicate that votes correlate with importance when they actually correlate to quality.
If a question is not worded well or is not clear it should be down-voted; but if someone miraculously provides the correct answer or the community likes it, the user should be rewarded. The up-votes from the good answer should not be shared or benefit the question in any way.
The answer is no. The votes have no direct effect on each other.
In regards to importance and votes - I would say this is not a correlation (or rather, I don't really understand what you mean by "important" in this context).
The fact is, if a question gets lots of upvotes, it will draw more attention - so any answers to it, by association is already getting more attention. So... it already happens.