Is the Concept of Particularity a Limit Concept?

That depends.

The term is ambiguous. 'Particularity' can be taken to refer to a category common to all particulars, whether concrete or abstract.  (Tropes are abstract particulars using 'abstract' in the old, not the Quinean, way.) The concept of particularity in this sense is not a limit concept.  We have no trouble conceptualizing the category of particulars.   We grasp this concept by grasping the concept of unrepeatability and we grasp it in tandem with the concept of repeatability which is the mark of universals.

'Particularity' can also be used to refer to that which makes a particular particular be the very particular that it is!  Socrates, for example, is a particular concrete particular, and so is Plato.  Categorially, they are the same, but numerically they are different.  'Particularity' in the second sense refers, not to a categorial feature, but to a particular's haecceity (haecceitas) or thisness. 

The concept of particularity in this second sense is a limit concept.  This is because our minds cannot conceptualize the haecceity of a thing. We cannot form a concept that captures the Socrateity of Socrates, that 'property,' if his haecceity is a property, that he alone actually has and nothing else could possibly have. Individuum ineffabile est.  That is, the particular qua particular is ineffable.  It cannot be conceptually 'effed.' This why Aristotle says that there can be no science of the particular as such.  A sensible particular is knowable, but only in terms of its repeatable features.  It is the suchness of a this-such that is knowable, not its thisness.  And of course every concrete particular is a this-such.

So the concept of particularity in the sense of haecceity is a limit concept.  We have a concept of that which we cannot conceive in propria persona. So there is no incoherence in the claim that haecceity is inconceivable, just as there is no incoherence in the claim that God is inconceivable. There is no incoherence due to the distinction between limit and non-limit concepts. But is haecceity a positive or a negative limit concept? 

If positive, then  the concept points beyond itself to something that is real. That is, it points to something  mind-independently in the thing  that makes it be that very thing.  If negative, then the concept merely marks a limit to our understanding.  If positive, there is something we cannot understand; if negative, there is nothing there to understand. 

Let us use 'ipseity' to refer to the haecceity of a person.  I cannot grasp the alter ego in its otherness. The concept of ipseity, then, is a limit concept. Now suppose you said that this concept is negative. You would then be saying that there is nothing there in the other person to conceptualize as opposed to saying that there is something there that cannot be conceptualized.  But surely I know that a person I love is an other mind, an other I, an other subject despite my inability to objectify this other subject as I would have to in order to conceptualize it.  I know this whether or not I have any clue as to how I know it.  So in this case we would have to say that the concept of ipseity is a positive limit concept.  It points to an unfathomable reality in the other person that is presumably the locus of his free will, moral worth, and spirituality. 

If God exists, then the concept of God is a limit concept in the positive sense.  If you maintain that the concept of God is a negative limit concept, then, at best, you reduce God to a regulative Ideal in Kant's sense which is tantamount to denying the existence of God. 

We will have to discuss Kant.