To expand (unauthorized) on Jeff's factual answer
- Will bounties have absolutely no effect on sort order? Yes
- If the answer is yes, then should they? No
The bounty system allows users to generate interest and attention for a question they care about. It also allows users to reward an other user they found helpful.
However, the bounty does not mean that the answer has more merit. Awarding a bounty to someone is barely more significant than adding an upvote to an answer. It simply means that one particular user found that answer very helpful.
The reason why this does not affect sort order is because the motivations of the user who set the bounty are unknown, and we have no way of knowing if the criteria they used to apportion the bounty are in line with the OPs technical question. A short example.
OP: How do I Foo?
Poster 2: If you have access to XYZ, you should [... long, thorough, excellent answer ...] and that will fix everything ever.
Lets say the OP marks Poster 1 as correct, because his question mentioned that he did not have access to XYZ. Some other person comes along and loves Answer 2, so they create a bounty and give it to that person. It appreciates the fact that Answer 2 is an excellent answer, but that doesn't make the answer more relevant than it was before.
The bounty system is a way for a user to reward another user, or recognize some helpful contribution. But votes are the way that we determine relevance to the question at hand.