They do, I believe. Without an item number, can't tell. The first one I picked was a belt buckle- ships for almost $11? Does it weigh over 16 oz? Anyway, there was only 1 way for this item to ship (clicked 'shipping' and nothing else was offered).
Officially, the default is that eBay will first show whichever shipping option you entered first.
At one point, eBay even might not show a potential buyer all of the options that you set up, but that policy might have been dropped: "eBay will now only show the most cost effective shipping services for a given delivery speed, hiding higher priced options. "
