<p>Can a LINQ enabled app run on a machine that only has the .NET 2.0 runtime installed?</p>

<p>In theory, LINQ is nothing more than syntactic sugar, and the resulting IL code should look the same as it would have in .NET 2.0.</p>

<p>How can I write LINQ without using the .NET 3.5 libraries? Will it run on .NET 2.0?</p>

No, because while you thought LINQ is really just syntactic sugar, it actually heavily used expression trees -- a feature absent in .NET 2.0.
That being said .NET 3.5 only builds up on top of .NET 2.0, and that's the reason why the IL doesn't look "different" or "special".
I do not see a reason why you shouldn't just install the .NET 3.5 Framework. Everything .NET 2.0 will work fine on it, promise :)