Do you mean under the overhang ("under their seating area")? Don't do it. You won't be able to get into the top drawer.

My island is small, with Marvel fridge drawers in the middle, and small drawers on either side. Behind the drawers are the sink cabinet on one end, and a pullout for boards on the other end. On the back of the island is a drop down table, so it's basically a table height deep shelf on hinged brackets, underneath a 6" overhang. I do feel warmth from the fridge on the soapstone ledge over the middle when seated at the table. It's not disruptive, but I try not to put the bread or chocolate right there, so they won't get stale faster. Similarly, I try to keep medicines/vitamins away. It's merely warm. Nowhere near hot. But I try to be careful.

Noise is another story. Marvel (best drawer configuration when I bought five years ago) is pretty loud when it cycles and mine is on a platform to fit right as the island is a bit higher than standard. The platform makes it louder. I keep a little TV on a little lazy susan on the island so I can actually look while prepping, and I often sit at the table side to relax in front of the TV while doing tedious things like cutting kale for chips, trimming artichokes, or shucking peas. The noise from the fridge bothered me a lot when it was first installed. It only took a few months, however, to get used to it. The mind can actually subtract a familiar sound like that from its perception of local sound, meaning I don't have to change the volume when it cycles (which I do for the washer which is ten feet away). I don't know if that means the washer is louder or just not heard enough to be familiar enough to be subtracted.

The table really only seats two, though more could crowd around, and even for two, we generally eat in the dining room, but on the few occasions when two are eating solo meals at the island that happen to coincide, I haven't noticed any interference with conversation or comfort by fridge noise. But "company" never eats in the kitchen, so it might just be that since we're used to the sound, we don't pay heed to it.

Vibration is no problem.

We have them in the base of a hutch built into our breakfast room. Mine are Perlick and are right behind me when I am sitting at the table. No noise, vibration or other issues with them being so near where we sit, but that is a little different than the use I understand you are considering.

Thanks guys. Plllog it won't be under the seating side with overhang. It just hit me since it's a fridge and the peninsula will be used for some small meals with kids, would there be any annoying issues that I didn't consider? I never thought of the heat! Do you think same would happen with granite?

Yes. If anything, soapstone is denser than granite. The heat isn't a problem, however. It really is just warm. Think of what you feel by any refrigerator. Towel out of the dryer. It wouldn't bother your kids or harm them. It might be enough to make the milk lose its chill faster.

Different fridges might exhaust in different directions. I believe (can't remember for sure) that the installation instructions for mine included having a void behind for the warm air. Some might have an active vent to the front, so they can blow warm air on your feet. :)

I really don't think you'll have any trouble if you put the fridge on the other side of the peninsula from the seating.