I would rephrase that, I would say "IF a man is ordained."  I would say that the schism occurred almost 1000 years ago, when validity of ordinations, sacraments etc., were not in question at all. But 1000 years is a long time for nothing to have changed in a schismatic religion, particularly considering all that has happened in these last 60 years. 

Neither Pope St Pius X nor Pius XII ever questioned the orthodox sacramental validity. 

Whether they are valid all the time is irrelevant.  The discussion presumes they are, because we’re discussing WHY they are valid.  Don’t change the topic. 

We can set aside whether or not the EO have, since the end of Pope Pius XII's reign or V2, made any changes to their ordination/consecration formulas, or to what they believe about those orders, that would render them invalid.

What is relevant is that the the Church has, at least up until PXII, held their orders to be valid. What is also relevant is that those orders, which the Church held to be valid, were illicit. They were valid but illicit. The Church did not "give permission" to the EO to perform them, the EO stole them. How can this "unite them in some way" to the Church if they perform these sacraments against the will of the Church

The validity of their orders is why you will find theologians saying that it would be licit for a Catholic in danger of death to approach them for absolution of sins. This is the only time you can say that the Church "gives permission" to the EO in particular to confect the sacraments. But it probably is not even correct to say that the Church "gives permission" to the EO, the letter from the Holy Office gave permission to Catholics to approach EO in danger of death. Besides, the EO don't care what the Church says. They validly yet illicitly confect the Eucharist, holy orders, and Chrismation all the time.