How do I know if an Android tablet supports Project Butter? As far as I know, Project Butter is just shorthand for versions of Android OS that have quicker touch screen response, close to the "physicalness" of iOS devices.

But how do I know if a particular Android device has it?

Will a version of the OS with Project Butter (for example, Android 4.1) have silky-smooth touch response on ANY device it is installed on?

I'd like to use the answer to this question to buy a lot (20) identical tablets on ebay, so hopefully there is a way to answer the question for a particular device without having it in my hands.
"Project Butter" is Google's name for the UI latency enhancements implemented in Android 4.1 Jelly Bean. Any Android device running Android 4.1 or later will have those enhancements.

Remember, though, that software is only part of what makes an interface smooth and 4.1 isn't a cure-all for lag. Slow hardware will result in a slow UI regardless of the OS. Your best bet is to find a tablet with 1) 4.1 or higher, 2) good specs, and 3) good reviews of its performance.