I am going to say "yes" bcause I think it happens all the time. In all walks of life. People self-correct.
I agree a lot of folks never reveal, but I don't think self-correction is automatic or complete for those who choose to keep it to themselves.
And human nature tends to avoid the toughest self-correction until after some consequences (sun screen after a skin cancer event, better exercise after a heart attack, better use of alcohol after a DUI, etc). Not everyone, but I think most people need to feel the heat of the flame before moving away.
My wife was never going to tell. She aimed to self-correct. She felt some consequences of betraying her own values. She realized the A didn't help her fix anything in her life. But all of that combined was only a half-measure. She didn't examine the reasons and felt comfortable with silently shifting the blame for her actions on me and the marriage.
Once she confessed, she learned so much more about herself and what elements she missed attempting to self-correct without any counseling or asking me if the feelings she projected on me were true during those years of the secret.
And as Strugglebus observed:
I don't think any relationship with a lie that big can truly be intimate.
This relates to the original question of can it be reconciliation without the truth?
I agree with SB. The very definition of intimacy to me is honesty and vulnerability.
The secret caused a substantial emotional rift, regardless of my wife's efforts to self-correct. She was able avoid additional infidelity on her own, but wasn't able to be all in -- when you withhold pain, it is tough to feel completely safe and 'known' to your partner. She was afraid the truth would end us.
Instead, the truth finally gave a chance to be so much closer than ever before.
And I'm grateful to have her in my life, flaws and all, because at least we're authentic now. Now she understands her poor choices with a clarity she couldn't find by herself.