Sean,
Do you distinguish between those who have no understanding of Tradition, and those who do, when it comes to the grace received from Novus Ordo Sacraments?
Indirectly:
If a sacrament is a sacrament, then the grace is contained in it ex opera operato.
But whether or to what extent that grace is efficacious in the recipient is determined ex opera operantis.
So, were a trad to receive NOM Communion, for some reason, he would probably receive very little grace (or none at all), as his disposition would be averse.