Can a dopamine agonist reverse the effects of an irreversible dopamine antagonist?
No. Irreversible antagonism is, by definition, inhibition that cannot be reversed by the agonist. Let me summarize the basics. You can read about this in Goodman and Gillman's The Pharmacological Basis of Therapeutics, Chapter 3, but there are many basic biochemistry textbooks that will cover the same ground.
When an interaction between a ligand and a receptor is said to be reversible, it means that it can associate to form a ligand receptor complex, and then dissociate, leaving the system with free ligand and free receptor. In the most general case, when the ligand is bound, it changes the conformation and activity of the receptor, and when it dissociates, the receptor returns to its original conformation and activity. The effect of the ligand in the biological system is related to the proportion of bound receptors.
Irreversible ligands typically involve covalent bonding (e.g., aspirin, alkylating agents). When the ligand interacts with the receptor, it irreversibly alters the conformation and function of the receptor. Cell or tissue function is only returned to the free receptor state when the particular receptors that have had a ligand receptor interaction have been degraded and replaced by a new receptor.
One of the ways to test whether an interaction is reversible is to try to reverse it. Let's look at how you would do this.
Start by looking at the effect when an agonist binds. The agonist is reversible. When you add it to an assay that contains the receptor, it associates and dissociates from the receptor, but at any moment, some proportion of receptors is bound to agonist. This binding produces an effect you can measure. The effect is related to the overall proportion of receptors bound to agonist at any given time, which is related to the concentration of the agonist. When you increase the concentration of an agonist, more agonist binds and you can measure a greater effect. In this figure from Goodman & Gillman Chapter 3, you can see the log concentration of the agonist on the x axis and the effect measured in an assay on the y axis:
Now consider the effect of an agonist in the presence of an antagonist. Classically, a competitive reversible antagonist binds the same site as an agonist. When the antagonist is bound, it doesn't allow the agonist to bind. So run the same experiment as you did above (by increasing the concentration of the agonist and measuring the effect), but start with a solution that contains some fixed concentration of antagonist. Because an antagonist is competing for those same binding sites, there will be fewer receptors available for agonist binding, fewer receptor/agonist complexes, and a smaller effect.
If the antagonist is reversible, though, you can still get the same effect you got in the first experiment. You just have to increase the concentration of the agonist until it binds the same proportion of receptors. Since both agonist and antagonist are constantly associating and dissociating with the receptor, increasing the concentration of one of them will out compete the other. In this figure (same source), you can see that in the presence of an antagonist (here, i, for inhibitor), it requires more agonist to get the same effect, but the maximum effect is still the same.
If the antagonist is irreversible you can't get the same effect you got in the first experiment, even by increasing the concentration of the agonist. The receptors have been permanently altered by the presence of the antagonist, and whatever portion of them had some interaction with the antagonist will either not bind the agonist, or will not produce an effect when bound. What you see in the assay here is that increasing the agonist concentration in the assay may increase the measured response, but you are unable to reach the same maximum response. Note here, the figure describes a pseudo-irreversible inhibitor (antagonist). This is just a term for an irreversible inhibitor that doesn't covalently bind the receptor, but has a strong enough affinity for the binding site that, based on the measurements, it looks like it covalently binds. Effectively, the inhibitor is going to sit there on the binding site until the receptor is degraded and will not be outcompeted by the agonist.