Can a spouse who has been put away for the cause of adultery, be reconciled to the innocent party if the innocent party so desires according to I Corinthians 7:11?
Of course. Jesus' statement in Matthew 19:9 is an allowance, not a requirement. A person dealing with a spouse who is committing adultery and refusing to repent of it has the option of ending the marriage. That ending allows the innocent party to remarry if he so chooses. But that includes restoring the marriage if the guilty party has given up his sin.
As a matter of fact, when I'm counseling people about martial problem, the goal is a successful marriage. In a few cases, when one side is repeatedly involved in sexual sin and refuses to stop, I'll tell the other side that they should consider divorce with the hope of it turning the guilty party away from sin. It doesn't always work, but it has turned around a few desperate cases.