Sure.
If the priest absolved him of the mortal sin, being let's say a sympathetic and very liberal priest, even if the sinner only confessed his sin but was unrepentant, then would the priest have the power to absolve the unrepentant sinner if he so wished?
If the sinner was unrepentant, the absolution would be as inefficacious as the Eucharist was to the sinner in the first place. One cannot receive the grace of any sacrament without the minimum disposition necessary.
On the flip side, what if the priest decided not to absolve him of the mortal sin, relying upon his own authority to 'retain' the man in his sins, having perhaps judged his confession insincere. This sinner, being unrepentant in his heart and his priest not having absolved him, then takes the eucharist. Has he then eaten and drunk irrevocable damnation?
No damnation is irrevocable as long as the future possibility of repentance is present.
But in the instance you've given, his decision to take the Eucharist despite not being absolved is another mortal sin compounding his already deep guilt.
Let's say the unrepentant sinner goes to a defrocked priest but one which still holds the priesthood since Rome holds that any conferral of priestly power is irrevocable even by Rome. So the corrupt, drunken pedophile ex-priest hears the insincere confession and absolves the still insincerely repentant sinner. Has this loosed the sinner from mortal sin and damnation?
No, for three reasons. First, the sinner is not truly repentant. Second, he has sought absolution from someone who is no longer permitted to grant absolution. Third, the only circumstances under which a defrocked priest's absolution can be validly given is if the penitent is believed to be on their deathbed.
Let's say this good priest knows the man is in mortal sin and knows that he has not made a confession. But the man comes for communion and the priest, knowing full well this unrepented mortal sin against the sinner, gives him the Eucharist deliberately and thereby give him damnation to eat and drink. Is that unworthy and damning communion in a state of mortal sin irrevocable? Has the priest, in effect, sent that sinner directly to hell by letting him take communion unworthily? Can the sinner ever repent again?
It is not irrevocable, but it is, as before, yet another grave sin superadded to the other sins.
That priest has committed a grave sin himself by helping the sinner to desecrate the Eucharist. But the priest did not hold a gun to the sinner's head forcing him to take the Eucharist - he's brought his own sin on his head.
The sinner can repent again. Christ never abandons anyone who turns from sin in a true desire to follow Him. The Church cannot deny a truly repentant individual the sacraments.