Having direct contact with some of the mercenaries would hopefully give him a chance to earn their trust at least to some degree, while maybe also being able to pick up on some information via listening in on the conversations they have amongst themselves. I assume they would be careful with what they said to each other in his presence (or when communicating with him about an op via implant), but are there any off-handed comments or other tidbits of information he might pick up on? Even if he doesn't have full context for them.

Jack would figure that there are tons of mercenary groups out there and that not all of them necessarily have any connection to the Displaced drop-offs or the kidnappings to the Gates, but in light of the monster event, he would bring up the Displaced as a general topic and try and gauge the mercenaries' feelings about them, to see if that reveals any possible connections to those topics or information they might have. What might he learn by doing this?

He wouldn't reveal himself as a Displaced right away with this set up, instead hoping to slowly learning more about the mercenaries via working with them, even if it's not directly.