Is it valid for a husband to take back his wife without her knowledge or intention, following a divorce by implication that she is unaware of, such that the husband pronounces the رجعة (return) to himself, or has intercourse with her intending the رجعة?

The wife's knowledge or consent is not a condition for the revocable divorce (raj'ah). The revocable divorce is effected verbally, such as by saying "I take my wife back," or by intercourse with the intention of reconciliation. It is valid without intention according to some scholars.