Could they have tried to saved it? Perhaps. Suppose McCoy just stunned it, then they call security to take it to the brig. It wakes up along the way and uses its hypnotic powers on the security guards, who then go the way of typical redshirts. Or they manage to get it into the brig, but it fools some weak-minded guard into letting it out (and then consumes said guard's bodily salts). Then the creature is running loose aboard the ship again, and the same thing keeps happening.
Kor
Why the brig? Why not the transporter room? Beam it down, leave it salt, warp out. Problem solved. While it was "McCoy," both the creature and Crater very clearly stated how it felt and what it needed. Ending it with a confrontation was probably the biggest concession to the monster/SF genre this episode made.
Had this episode been written or shot at after the mid point of season one, the climax would have been totally different.
Would Spock have suggested using a truth drug on Crater?
Would Kirk have been such a nasty bastard toward the Professor at that time?
Would Kirk have showed up alone in McCoy's quarters with a phaser and a few salt tablets?
Would Spock have run in right after, shrieking like a lunatic and whaling on "Nancy" with both fists? (I admit I loved "proto Spock")
Would McCoy have used the kill setting (although it was resistant to "kill" so maybe it wouldn't have done much good)?
I'd venture to say "no." Just look at "Devil in the Dark." It was practically a reworking of this episode, only with the more enlightened point of view the series became known for.