I’ve served on a jury twice and called for duty four or five times. They didn’t ask me about any illness at all, mental or otherwise. They did ask about my occupation. I can’t get into the details, but I feel my experience with my illness was relevant in both cases, and if I hadn’t served it may not have been fully a jury of peers.
I don’t think it changed the adjudication either way, as the only relevant thing was being able to interpret the law and follow instructions. Laws generally don’t take SMI into account unless in rare cases where insanity or guilty but insane defenses are employed. I was not involved with any sentencing, my experience may have been relevant in that case, but that would depend on the instructions and sentencing guidelines.
Generally you are encouraged to speak with the judge privately if there’s a possible issue with you serving. I had prior knowledge of a newspaper article about a case in question, so I spoke to the judge about it, and he asked if it would interfere with applying the law and following instructions and I said no.
Bear in mind that there’s also a minor amount of voir dire questioning from the lawyers, but it’s very minimal. I thought it was a good experience and I was paid a token amount for my time (I didn’t cash the checks, as my employer paid for the jury time) If you don’t think it might trigger him in some way, as there is the potential to see difficult crime scene evidence and testimony, and you think he can think clearly enough to interpret the law and jury instructions, I would leave it to the judge to decide.