Well as mentioned in the comments with the passing of each Yuga there is a general degradation of the morality however Kali and Dvapar have worked in cahoots before so I wouldn't discount the possibility of what you are suggesting.
SECTION LVIII of the Vana Parva of Mahabharat mentions the following episode:
"Vrihadaswa said, 'When the blazing guardians of the worlds were returning after the daughter of Bhima had chosen Naishadha, on their way they met Dwapara with Kali approaching towards them. And seeing Kali, Sakra the slayer of Vala and Vritra, said, 'O Kali, say whither thou art going with Dwapara.' And thereupon Kali replied unto Sakra, 'Going to Damayanti's Swayamvara, will I obtain her (for my wife), as my heart is fixed upon that damsel.' Hearing this, Indra said with a smile, 'That Swayamvara is already ended. In our sight she hath chosen Nala for her husband.' Thus answered by Sakra, Kali, that vilest of the celestials, filled with wrath, addressing all those gods spake, 'Since in the presence of the celestials she hath chosen a mortal for her lord, it is meet that she should undergo a heavy doom.' Upon hearing these words of Kali, the celestials answered, 'It is with our sanction that Damayanti hath chosen Nala. What damsel is there that would not choose king Nala endued with every virtue? Well-versed in all duties, always conducting himself with rectitude, he hath studied the four Vedas together with the Puranas that are regarded as the fifth. Leading a life of harmlessness unto all creatures, he is truth-telling and firm in his vows, and in his house the gods are ever gratified by sacrifices held according to the ordinance. In that tiger among men--that king resembling a Lokapala, is truth, and forbearance, and knowledge, and asceticism, and purity and self-control, and perfect tranquillity of soul. O Kali, the fool that wisheth to curse Nala bearing such a character, curseth himself, and destroyeth himself by his own act. And, O Kali, he that seeketh to curse Nala crowned with such virtues, sinketh into the wide bottomless pit of hell rife with torments.' Having said this to Kali and Dwapara, the gods went to heaven. And when the gods had gone away, Kali said unto Dwapara, 'I am ill able, O Dwapara, to suppress my anger. I shall possess Nala, deprive him of his kingdom, and he shall no more sport with Bhima's daughter. Entering the dice, it behoveth thee to help me.'"
Again as per SECTION LXVII of the Sambhava Parva of Mahabharat Duryodhan himself was an incarnation of Kali:
The evil-minded and wicked king Duryodhana, the destroyer of the fair fame of the Kurus, was born of a portion of Kali on earth. He it was who caused all creatures to be slain and the earth to be wasted; and he it was who fanned the flame of hostility that ultimately consumed all. They who had been the sons of Pulastya (the Rakshasas) were born on earth among men of Duryodhana's brothers, that century of wicked individuals commencing with Duhasasana as their first. And, O bull among the Bharata princes, Durmukha, Duhsaha, and others whose names I do not mention, who always supported Duryodhana (in all his schemes), were, indeed, the sons of Pulastya.
The Mahabharat thus clearly states that it was Kali in the form of Duryodhan who fanned the hostilities and caused the death of thousands of creatures.