No. It's allowed and you won't get banned. If one of the accounts get banned for what ever reason though expect the other one too as well.
Bounty activities is not one of the reasons that gets accounts banned right?
Participating in bounties with two accounts isn't going to get you banned off the forum. Although, you would need to look into the bounties terms and conditions as they may not want people from the same IP/household participating. If you are found to be abusing bounties with multiple accounts you may receive a negative rating from users of the forum.
That's very reasonable. That's basically what I had assumed. You are no fool, theymos, and I was pretty sure I would have no problem with how you view these situations. I remember I played an MMORPG about 10-years ago and they wanted to ban a single hacker from Brazil, but what ended up happening is an accidental ban of multiple others. This was due to the situation you describe, and so I'm happy that you acknowledge how poor of an identifier IP addresses are.
The italics around "automatically" do tell me that accounts sharing the same IP will be under sure scrutiny, unless I've read the implications incorrectly. It might be redundant to even say that, but thanks for the clarification - straight from the horse's mouth.
I think it's fair to assume that when an account is banned others which share a common IP will be looked at. Although, there's ways of telling whether someone is an alt account of another through various different methods. If the staff have only a common IP associated with each account then the other one will not be banned just because of that. Looking at my first reply it probably needed to be explained a little more.
I was initially referring to alt accounts because of the way the OP is phrased and the problem with using two accounts and one of them getting banned and you continue to use the other which the other account would then be banned for ban evasion.