Can overheating damage the engine sleeves?

Thanks for replying hmac300. What you said makes perfect sense. The reason I'm asking this is because I live in Brazil and down here labor for this car is quite expensive. I drove it under this condition only once. I caught by surprise and had to keep going for lack of alternative and the car actually made it to my appointment. After it cooled down to normal running temperature I tried adding water and saw vapor coming out of the tail pipe (on a warm day). After that I never drove it again and sent it to the mechanic. The problem is the labor for taking it apart for the head gaskets job already cost $2000 and dismounting it further down just to check the possibility of its sleeves' lower rings being damaged would set me back another 2000. If he puts it back together with all the upper part done and it ends up mixing oil and water, all the previous labor of taking it apart and putting it back together will be wasted and the expense will be even higher.
So, I was hoping anyone could tell me the likelihood of this kind of damage happening to the lower part of the sleeves of this engine due to overheating because, unfortunately for me, otherwise it will be kind of a lottery deciding on whether to close it without checking.
Thanks again.

@ fixitmr Because down here car prices are absolutely insane. A 1996 just like mine goes for 17k! A brand new one is 130K. And everything else in my car is perfect working condition, brakes, transmission, suspension, tires, body work, interior. Just like new.

@ mhpautos Thanks for the reply. According to my mechanic, it's a wet sleeve engine. That's why the concern about the seals at the lower end.

Thanks to all the help I got so far, I can rephrase my question, being more specific:

- What is the chance of overheating damaging the lower seals of the the wet sleeves of a Nissan VQ30DE engine?

It's been driven without coolant and overheated but did not shut down. After turning it off and letting it cool down, I realized vapor would come out of the exhaust at normal running temp on a warm day, so I had the heads removed.

Thank you all.

@ fixitmr Thank you very much for all the replies, I really appreciate it. I'm checking on the dry/wet issue and then share the information. I'll try and see one of those sleeves myself or do a research on the net about the VQ30DE. But I'd be surprised if the mechanic were trying to push this on me. He's been working on the family's cars for a while now and has had a fairly honest approach on dilemmas like this so far. I really hope I'm not mistaken!