According to Evangelicals, will the saved ever experience the magnitude of suffering associated with their sins? On another website, one person said this concerning Catholicism and Purgatory,


  My own vision of purgatory, for which I claim no doctrinal validity, has some interesting echoes in the platonic version (which I have never seen till now.) It is that we are shown for the first time the true evil of our sins, and especially the wide ripples of harm our sins caused to others. We thus endure an excruciating revelation of the evil we have perpetrated, and are invited to full repentance, which probably includes going to each person we wronged and obtaining pardon.


Whether that is true or not is not important. 

My question to Evangelicals is this:


Will one who is saved, that is, one who has faith in the Lord Jesus
Christ, ever experience the magnitude of suffering associated with the sins he/she committed (especially against others) in this life, as well as know (by being reminded of) all the sins they have ever committed (i.e., the total quantity)?


  In order to know all the sins they have ever committed, imagine a courtroom where a judge is reading a list and judging you guilty of every single sin you have ever committed. Moreover, by experiencing the magnitude of suffering associated with each sin, imagine each time a sin is enumerated by the judge, you experience (feel) the pain, anguish, hurt, and sorrow felt by the person you sinned against, as well as your very own soul (when you have sinned against yourself). Catholics experience this in Purgatory, and their souls must be purified of their sins.

If so, when does this occur and for what purpose?
Or, does God forget them (cp. Jer. 31:34) and the saved never experiences them in judgment?
I am an evangelical, but am not entirely sure if my belief is the official stance of the church. 

Concerning your first question, I believe that when we see God, we will know the magnitude of our sins. Similar to how Isaiah did: 


  "And I[Isaiah] said: “Woe is me! For I am lost; for I am a man of unclean lips, and I dwell in the midst of a people of unclean lips; for my eyes have seen the King, the LORD of hosts!"(Isaiah 6:5 ESV). 


Thus, yes, when we get to heaven, we will see God, feel the magnitude of our sins, and be disgusted by them. And knowing what sort of persons we are in the eyes of God, thank him all the more for the grace which he bestowed upon us, and the love with which he loved us.

The purpose of this is to bring Glory to the Lord, for on earth, we never know the magnitude of our depravity, but once we see the Holy God, whose countenance is so pure he cannot even look upon sin we can understand the magnitude of the grace with which He saved us.  

You mentioned at the end of the first bullet, "especially sins committed against others". I would like to make the argument that a sin committed against God including other sinners is no worse than a sin committed against God when we are alone. For sin is the state of rebellion against God, so although we hurt people, we never actually sin against people.  


  Against you, you only, have I sinned and done what is evil in your sight, so that you may be justified in your words and blameless in your judgment. (Psalm 51:4)


Concerning your final point, The Lord Jesus Christ has justified us via his death on the cross. Where 'justified' is used in the most legal sense - that is, God treats us as if we had never sinned, as if we were righteous.


  But to the one who does not work, but believes in Him who justifies the ungodly, his faith is credited as righteousness (Rom 4:5) 


I don't know if it's correct to say God 'forgets' our sins. But it is to say his righteous wrath upon our sin was satisfied by the death of the Lord Jesus Christ. And through Christ, he has removed our sins from us.


  "as far as the east is from the west, so far has he removed our transgressions from us." 


Sorry if I was a bit long winded. But I hope I answered, or at least provided some insight concerning, your question.