So for example, the Nicholas Romanov family, who were very recently canonized by the Russian Orthodox Church, would be recognized by the Catholic Church as true saints?
That's a tough question.
As Father Z said, the practice in the Catholic Church is to "normally recognize the Orthodox Saints". This has been most obvious when various Orthodox communities have entered into union with Rome, forming the Eastern and Oriental Catholic Churches. Typically, Rome has made no demands on these groups that they cease commemorating or venerating those whom they have traditionally honored as Saints, except in a few rare instances where the individual was so antithetical to Catholicism that it would fly in the face of reason to have him or her venerated by Catholics. I'd give you an example, but my brain isn't functioning right now. (I would note that the Ethiopian Tewahado Orthodox venerate Saint Pontius Pilate, a commemoration that the Ethiopian Catholic Church was required by Rome to expunge from its calendar when the former entered into communion with Rome.)
The Romanovs are of a category of sainthood referred to by the Orthodox as "Passion-bearers", loosely defined as Christians leading exemplary lives who suffered a violent death but not directly for the Faith and thus not defined as "martyrs", in the traditional sense. It's not a classification of saints currently known to Latin hagiography. However, Rome's own understanding of martyrdom, often thought of only in the context of death for the Faith, actually includes 5 categories of martyrdom:
- in odium fidei
from hatred of the faith
- in defensum castitatis
in defense of chastity
- ex aerumnis carceris
from the hardships of incarceration
- per testimonium caritatis fortis
by witness of heroic charity
- ex acertatibus et vexationibusque pro fidei quibus pertulit
by reason of the force and violence which were endured for the faith
As Rome typically has taken the a generous viewpoint with regard to veneration under a local cultus
, I suspect that nothing would be any different in this case. There were, in fact, Catholic hierarchy present at the liturgical ceremonies in which the Russian Orthodox Church declared the Romanovs to be canonized.