All other things being equal, yes.

There are two primary reasons why this is so.

• To maintain the same amount of field intensity of light over a larger area, a lens used with a larger sensor has to be able to collect more total light than a lens used with a smaller sensor. This means a larger entrance pupil, which usually works out to require a larger front element.

• The larger the sensor, the longer the focal length of a lens needs to be to give the same Field of View (FoV), and the larger an image circle it needs to project. On a compact camera with a small 1/1.6" sensor, a 50mm lens gives the same FoV as a 215mm telephoto lens does on a 35mm film camera. On an APS-C camera, a 50mm lens results in an FoV that is in the beginning of the telephoto range for a 35mm camera, 75-80mm. On a 35mm camera a 50mm lens is considered normal, because the focal length is very near the registration distance of the camera and because that focal length is roughly equal to the diagonal measurement of the plane that records the image. A medium format camera will give an FoV using a 50mm lens that is about equal to a 32mm lens paired with a 35mm camera. On a Large format 4X5 camera a 50mm lens gives an FoV about equal to a 13mm lens on a 35mm camera.
  a) Especially with longer focal lengths, the physics involved are hard to overcome. Although the strict technical definition of a telephoto lens is one that is designed so that the distance from the image plane to the front of the lens is shorter than the focal length of the lens, there is only so much one can do in reducing the size of a lens with a long focal length. This is especially true if the cost to produce such a lens is considered.
  b) Just as a 50mm lens used on a 4x5 camera must project a light circle considerably larger than the light circle cast by a 50mm lens designed for a 35mm camera, lenses designed for smaller sensors can project smaller light circles. This allows the lenses to be smaller in diameter. It also allows them to be made with less quantities of some of the most expensive materials used in a lens: the corrector element at the rear of the front group.

So a 50mm lens designed for a small compact can be both shorter and smaller in diameter than a 215mm lens that gives the same FoV on a 35mm camera. Even in terms of Micro Four-Thirds sized sensors, only a 100mm lens that throws a light circle slightly larger than 22mm is needed to provide the same FoV as a 200mm lens throwing a light circle at least 44mm in diameter on a full frame camera. An APS-C camera would need a 125-133mm lens with a 27-29mm light circle, depending on whether it is a Canon APS-C or Nikon/Pentax/Samsung/Sony.