I've just bought the Logitech anywhere mouse and I was wondering if I use the mouse on wet surface area will it spoil the mouse?
The "anywhere" refers to the laser/sensor type used to track the mouse movement. Traditional red laser mice do not work very well on semitransparent, transparent, or excessively shiney surfaces (a glass desk, a piece of clear plastic on top of your desk, or a highly polished wood desk), as well as on non-flat surfaces (your leg), heavily textured surfaces (your couch). Their optimal working area is a dull, slighly textured surface, such as an unpolished wood desk, a painted desk, or a mousepad. By using more sensitive camera sensors and light sources that work differently than normal visible light, an anywhere mouse (and most high-end mice today) can work just as well on any of these surfaces.
The assumption is simply that the surface is stable (ie, not liquid) and has the physical properties of a solid collection of matter (anti-matter and dark-matter are generally regarded as being singularly imperfect mousing surfaces). Even then, transparent surfaces that have a light source under or behind them will still probably stymie even this anywhere mouse, especially if the light source emits non-visible light similar in wavelength to that used by the anywhere mouse.
By anywhere they mean solid surfaces. In their web page, they say:
...tracks on surfaces like clear glass* and lacquered desks that stump optical mice and standard laser mice.
*At least 4 mm thick.
If you had a normal base, like a desk, and it got water on it, I do not think that a small film of water is going to affect you. I base this on having used optical mice on desks with glass tops, which were much thicker, and still worked well.
That said, I would not recommend it since you are talking about water and an electrical device. When I say that, I am not worried about electrical shock from +5V DC, but simply that you risk ruining it unless you can somehow really waterproof it. I would also worry more that your "waterproofing efforts" would cause more problems optically with the mouse than the water itself.
As long as any of the electronics in the mouse are not exposed to water, there should be no damage to the mouse itself. The plastic casing should protect the mouse from a modest amount of water, but submerging it underwater is likely to destroy the mouse. That being said, it is still unwise to use any electronic devices in areas where they are likely to come into contact with water.
Whether or not it actually works (i.e. tracks the wet surface), however, is a matter of the construction of the mouse itself, specifically due to the implementation of optical sensor technology it uses.