The short answer is, yes. I can cite two examples:

I had a long-term (5 year) relationship with a man who cheated on me during the first 6 months of dating, I chose to forgive as ultimately he chose me and I thought we had something special. We broke up due to unrelated reasons and he didn't date anyone else after me for the ten years until he sadly passed away.

A close friend of mine had a short affair (around three months) after five years of marriage. Her husband chose to forgive her and 2o years later they have never been happier.

I suppose it depends on the strength of feelings each party has for each other. I chose not to forgive a different boyfriend for cheating as I didn't think the relationship was right for me.