You’re really asking 2 separate questions:
- Does the Holy See have the authority to allow a married man to be ordained?
Yes. See Canon Law below:
Can. 1042 The following are simply impeded from receiving orders:
1/ a man who has a wife, unless he is legitimately destined to the permanent diaconate
Can. 1047 §2. Dispensation from the following irregularities and impediments to receive orders is also reserved to the Apostolic See:
3/ the impediment mentioned in ⇒ can. 1042, n. 1.
- Is this authority ever exercised?
Yes, under certain conditions which have already been covered.
No, if the cases you mean are e.g. a lifelong Latin Rite Catholic, a lay convert, a ministerial convert who was not married at the time of conversion etc.