Is the silent treatment a way to deal with a cheating partner?

That isn't the correct way to deal with a cheating partner. If you know your partner is cheating, and if you still want to make it work than you should probably separate for a for a while, but inform your partner that you still want this relationship to grow. Also you should ask the cheating partner is they want to make something out of the relationship. That is my best advice. Or see a therapist.