What a cavern class will give you is a better understanding of the issues. Taking the class may make you somewhat less likely to jam a reel or get entangled in your own guideline. Taking the class and doing well may make you a bit less likely to blow the viz, if you wander into the wrong passage by mistake and get into the silt. And if your instructor is persuasive, clear and compelling, you may understand why going into a cave with a single tank and a single regulator is a gamble most people are unwilling to take.
It appears that you really want to do this dive -- I don't know why; I don't find either the slot at the Ear or the rocky passage out the Eye to be compelling, especially compared with other sections of that cave. But you've been offered a class that CAN make something you want to do, which is inherently too high risk for most of us to contemplate or recommend it, somewhat less dangerous, and if you take Superlyte up on his offer, you might find you actually ENJOY the training, and even find it improves your open water diving. And you might also find that you like the cavern environment enough to want to get the training to do the dive you contemplate -- and much more -- with the greatest degree of safety that such dives can have.
I like the way AJ put it -- just going into the cave puts you a little way into the incident pit. Most people think those of us who cave dive are crazy, and they may well be right. But if you are going to do something which seems absurdly dangerous to the rest of the world, it just seems reasonable to do it as safely as it can be done, and the training programs have a pretty good track record of allowing the majority of people who go through them to cave dive and survive it.