Fob, when I put myself in that equation, I don't think I would entrust the information with them.
This kind of thinking runs counter to a mode of thought we're supposed to have when we are quitting, I suppose. We're supposed to be honest and transparent and sticking with facts, and that would be good exercise against all the negotiating our brains can do ("it'll be better, it wasn't that bad..." - all those potential debates).
But I look at the non-disclosure as a necessary form of survival. If you can continue with your current job and still make the personal progress in your recovery, then that's one way of looking at it. If you think you would not be successful, then maybe that changes the name of the game a lot more.
I quit a job while I was doing rather well because I had aspirations about moving on to do other things. I quit drinking a week or two later, and then everything shut down (my ambition, my gumption, my courage, my energy - it was all zapped). I made progress personally and eventually started to get into the new career stream months later, after an uphill search battle. And all that only to arrive at not caring about the new career stream after all. So I let go of that. Now I'm in trouble and am looking again on the work path that I already had. It's a bit of a slap in the face for me (aren't alcoholics supposed to lose everything before they quit?); but so far so good as far as my resentments impacting my behaviour go. There's a sting there, but not the kind that feeds an interest in drinking.
I noticed you might resemble me intellectually or emotionally in some ways. If you're like me, it might be worth it to avoid situations when you are tempted to analyze too much - to your detriment, maybe. Sometimes it works out so much better when you race to the conclusion rather than building the proofs, which feed a hunger for more problems to solve, more challenges, and more saga. Earlier instincts about what to do might just be right most of the time. So if you're accurate about the "paralysis by analysis" tendency in you, try to find a happy medium. I don't know if I am at a "medium" right now, but what I do have is no drinking and that much to consider successful.