You can use any image as a texture, like ndchristie said. So yes, technically, you can apply a sprite as a texture on a model.
However, the most important information in a sprite tends to be the shape and colors, not so much the "texture" in itself. Good pixel art usually goes to extreme lengths to imply the shape of the object via light and color information. Those are things that, in 3D, become pretty much obsolete, and can make a model look worse, in fact, if applied inappropriately. If you want to use pixel art as texture on a model, it needs to be made with that in mind, like some others here in the Low Spec section. I'd be pretty much impossible to grab a sprite and slap it on a model and have it look good.