B.B. Warfield seemed to think so when he said: "Thus it comes about that the doctrine of monergistic regeneration -- or as it was phrased by the older theologians, of "irresistible grace" or "effectual calling" -- is the hinge of the Calvinistic soteriology, and lies much more deeply embedded in the system than the doctrine of predestination itself which is popularly looked upon as its hall-mark. Indeed, the soteriological significance of predestination to the Calvinist consists in the safeguard it affords to monergistic regeneration - to purely supernatural salvation. What lies at the heart of his soteriology is the absolute exclusion of the creaturely element in the initiation of the saving process, that so the pure grace of God may be magnified. Only so could he express his sense of man's complete dependence as sinner on the free mercy of a saving God; or extrude the evil leaven of Synergism (q.v.) by which, as he clearly sees, God is robbed of His glory and man is encouraged to think that he owes to some power, some act of choice, some initiative of his own, his participation in that salvation which is in reality all of grace.” (link)
I disagree with Warfield or at least have some doubts that the terms are equivalent. Setting aside the fact that regeneration is more specific than grace, it just appears that that irresistible is broader than monergism and relates to more parts of the conversion process. Per the Calvinist order of salvation, God regenerates, then calls then man repents and believes. God’s regenerating and calling guaranties a response. It’s the aspect of guaranteeing repentance and faith that is included in irresistible grace, but missing from monergistic regeneration.
Does this seem like hair splitting? Maybe it is, but the term monergistic regeneration has lead to a good deal of confusion. For example, do I hold to monergistic regeneration since I think God alone regenerates man, even though I think regeneration happens after faith, not before? Many Arminians do view themselves as monergists on this account. But if Calvinists insist that repentance and faith in response is regeneration is a vital aspect, then are Calvinists synergists because man is active in repentance and faith? But perhaps monergistic regeneration must be a regeneration that takes place at the initiation of the saving process. Well, in that case do Arminians hold to monergistic previenient grace and they therefore are also monergists? After all, it’s Pelagians and Semi-Pleagians, not Arminians who deny that God alone initiates the saving process.
On this account some Calvinists drop regeneration and just speak of monergism. And there is a sense in which all Calvinists are monergists and no Arminians are: God determines the salvation of certain individuals. But the practical problem with this definition is that not all Calvinists use it and use it consistently and monergism is often still brought up in reference to regeneration and the order of salvation.
So in short, I think that the term monergistic regeneration is a poor improvement on the term irresistible grace.