Is sugar a thickening agent?

While sugar makes a liquid thicker, it is not considered a thickening agent.

Sugar is a crystal. When you add it to water, what you get is a simple solution. A solution of a solid in water is always thicker than water. This happens with all kinds of everyday substances. Whenever you add a thick liquid or a solid to a thin liquid, the result is a semi-thick liquid. The "thickening" here is roughly proportional. In that sense, you are not thickening the thin liquid, but creating a mixture whose thickness is the average of the thicknesses of its components.

A thickening agent, on the other hand, really thickens. It does not dissolve in liquid in the sense that it breaks down into ions swimming freely among the polar water molecules, but creates a hydrocolloid, also known as a "gel". This is a very special phase combination in which a few solid strands of matter trap lots of liquid in such a way that the liquid cannot flow easily. This results in a thick consistency.

Because a single molecule of a hydrocolloid building substance can trap lots of water, you can add little amounts of this stuff to create really thick liquids. Starch is added at a ratio of about 1:10 to create pudding, and some others such as xanthan can be used at ratios as low as 1:200 to create a creme and 1:1000 to create a milky-thick liquid out of water. At these consistencies, they rarely have consequences for flavor or nutrition, but really change the texture of your food. This is opposite to dissolving solids like sugar: if you wanted to add enough sugar to get your solution to a milky-thick consistency, you'd have an unbearably sweet liquid. For achieving a creme-like thickness, you actually need a supersaturated sugar solution, which is basically a candy (you'd have to stop heating somewhere below the soft ball stage).

So, while sugar does thicken somewhat, you will not use it for the purpose of thickening. If you were to choose the amount of sugar to add based on how thick you want your food, you will change all of its other properties, starting with making it overly sweet. The exception is when you are making candy: here, you are really using the thickening power of sugar, and you are controlling the amount of sugar such that you get the desired final consistency. Another exception is making jam - while it also has pectin together with the sugar, the amount of sugar is high enough that it also contributes a lot to consistency.

The viscosity of sucrose (sugar) solutions goes up quite rapidly as you increase its weight percentage over about 65%. Pure maple syrup runs about 60% sucrose. Unless you're looking to make something horribly sweet, sugar does not make a good thickening agent.