It's a no win situation.
Sometimes cheaters will come clean because of the "guilt" they may be carrying around. This is especially true if it was a one night stand they had because of circumstance or a unique opportunity presented itself. They simply can't look their happy loving spouse in the eye without it eating at them. Their candour is actually a way to get the monkey off of their back.
If a scenario is such that their mate has suspected them of cheating and has been pressing them until they finally confess it's highly unlikely the truth would be appreciated because the so called "honesty" came as a result of pressure.
Another factor to consider is the "intention" of the cheater. Most people automatically assume the cheater will beg for forgiveness and want to work things out. However there are just as many who "drop the bomb" as a way of ending things with their mate. It's not unheard of for a cheater to announce he/she is in love with the other woman/man.
Regardless of the circumstances it's practically impossible to "appreciate" being hurt and betrayed. The time for honesty was when the person felt like they needed something outside of their primary relationship. It's hard to give someone "points" for candour after the fact.