I should think the answer would be obvious: Kirk would seduce the Borg Queen. He would put her in touch with her humanoid side and she would let the Enterprise go. Afterwards, McCoy would say, "Dammit, Jim, I'm not even gonna ask anymore!"
But in all seriousness, I think compared to how much more advanced the Borg are to Picard's Enterprise at their first encounter, Kirk's Enterprise would stand about the same chance. Both ships use Phasers and Photon torpedoes as primary weapons; Picard's are simply more powerful. In the end, like Picard's Enterprise, I believe Q (or in Kirk's case, Trelane?) would have to intervene and save Kirk's ship.Depends upon what type of Borg vessel encounters the Enterprise and when it occurs. If it is a vessel containing the Queen during the first 5 year mission, odds are that Kirk would try to seduce/endear the Queen to him and upon failing that he would use a logic puzzle to make the Borg destroy themselves. If encountered during the movies they'd probably drive the Enterprise into the cube in a poorly conceived suicide run.He would have taken off his shirt and seduced the Borg Queen.