While it's difficult to give an answer that applies to all vinyl siding installers, I'll say this: in general, yes, you can expect the installation company to dispose of the current siding. Will there be a fee? Yes. Keep in mind that the installers have to do something about it once it's in their trucks. Whether they landfill it or stick it in their dumpster, it will cost them something. Either the fee will be invisible in the cost of your project or the installer will come out and say, "It will cost 'X' amount to get rid of your old siding."
In short, the siding won't be laying around in your yard after the project is done.
Recycling Vinyl SidingThat said, is there any better way of disposing vinyl siding than landfilling it? Way back in the dark ages of recycling, Principia Partners issued a prescient report with the exciting title of, Post Industrial and Post Consumer Vinyl Reclaim. Don't let the name fool you. It's actually quite riveting, if you have any kind of interest in home renovations and the environment. Another group, the Vinyl Institute, maintains an extensive directory of vinyl siding recyclers.
But don't expect your vinyl siding installer to take the siding to a recycler. They're thinking about cost-efficiency, and trucking waste siding to a collection facility 40 miles away doesn't return a single dime to them. Sorry, that's reality. Even begging the installer probably won't do much good. At this point, the only way to get your waste vinyl siding to a recycler is to either go with an installer who advertises recycling as a part of the normal process...or to haul the stuff to the recycler yourself.