Phantom Doctrine: Should I try to kill enemy agents when possible, but they are no threat during mission (and capturing them is not an option)?

Enemy Agents are persistent in the game world. They earn experience and grow in power just as your Agents do, and they run missions to help the AI opponent accomplish its goals. Whenever the AI is doing things like trying to kill your informants or searching for your base, it's using its own roster of Agents to do that. Thus, killing them in the mission does give you one advantage - the Agent is dead and no longer helping the AI defeat you. This slows down the AI's progress for a little while.

Of course, the AI will hire new Agents, just as you do, so the advantage is temporary.

Later on you'll be able to question them more deeply, implant trackers to follow them back to their base, and even brainwash them to turn them into double agents you can use on the battlefield. However, IIRC, even at this early stage the "questioned and then killed" result which you mention means that you get a little new information for your corkboard AND remove the enemy Agent from play. (It's a minor bonus, but it is something.)

But yes, killing them in the field does help you somewhat. I don't think them being exposed or not makes much difference specifically regarding the question of killing them in mission. Agents being exposed is something that hurts them on the strategic map, not the tactical mission map.