Influence is pretty huge, but hunters can be as helpful and as well as a disaster for a project. If an ICO restricts to pay their earnings, the bounty hunters will destroy the image of the whole project and the team.
Well, it is up to the team as to how they would treat the bounty participants because if they would just do what they promise then the bounty participants would do their job in promoting the project and then if they would decide to not pay them then it would just reflect that they may just be a scam team and their intention is really to just get money from people and then run away thereafter. Bounty participants are influential because they are the key so that the information about the ICO can reach as many people as they can.