Would you hook-up with a friend's conquest?

Nothing wrong with sloppy seconds, as long as boundaries aren't crossed.

If I knew he had something that I wouldn't want to catch, then maybe not.

It depends. If the friend was still pursuing that "conquest", then it would be pretty awkward.

Hmm...there's a slight chance that you will become the third person in the relationship though. Sometimes your friend might not say what they want and it is a bad assumption that the previous relationship is already over.

If it's someone who your friend is dating at all and you are looking only for physical gratification I wouldn't do it. Even if it is only casual dating, it could possibly change into something more, or maybe he wants it to be something more. It's just not worth it in my opinion.