Yes, if you don't seal it.
Wood is an animate thing, some species like oak or pine can move as much as 1/4 of an inch. What this does is cause severe warping, checking or splitting, the result of one side drying faster than the other and the resultant stresses introduced along wood grain. Throughout its use, wood will always move. Either alot or a little, it depends on if it was kiln dried or not, how humid or dry an area live in, temperature fluctuations etc. Warping is minimized by sealing the wood thoroughly, essentially cutting off its ability to breath and have variations of moisture content. Most plaques like many use for bases, like walnut or maple, are kiln dried then sealed prior to their commercial use as plaques, trophy stands, or in this case diorama bases. The harder the wood, the less movement (except oak which can be a happy wood when it wants to). But remember to treat any bare wood you might use first to minimize damage from the celuclay or other ground materials.
Plywood, is more stable. Since it is layers of wood with grain running perpendicular to the successive layer, the stress is kept to a minimum and spread out along the surface. This with the use of extremely strong glues and resins to laminate the layers keep it under control, and movement from expansion and contraction is kept to a minimum, almost negligible. But not all together impervious. (throw a piece of plywood out in the yard and see what happens...) Its draw backs are simple in that the edging must be covered to make for a more aesthetic presentation. This can either be done with picture frames, moulding or quarter or half round, dependent on your skill level and access to tools. Any cutting or routing you do must have sharp blades because the laminate layers are so thin you will get an amazing amount of tearout along the edge. Run a piece of masking tape across the edge you are cutting and it will minimize the tearout. You can still see your trim line through the tape and it will make for a cleaner cut. I actualy use a utility knife to mark my cutting line. It scores the grain at the intended edge and makes for a very clean cut. Also use a blade for plywood. The smaller/finer teeth make for a cleaner cut.
Since there are plywoods of almost every species of available woods, some very attractive bases can be made. Again seal the base first then use your ground material.
My favorite is MDF, medium density fibre board. This stuff is essentialy a wood pulp and fibre composite used in the mass produced furniture industry. Not particle board which uses small chips of wood pressed together and not melamine which is just finer chips of wood pressed together, this stuff is a fiber. It accepts laminates, and laminate composites very handily for different effects. It can be tooled (edges with a router) for some very nice edge detail and because it machines smooth it needs almost no sanding to smooth out machine marks. It is stable, heavy and makes for a very nice base. My suggestion though that because it is a composite of wood and paper fibres, that you seal it before you apply your celuclay. As it will swell and make surface blisters if it is made damp. A polyeuathane or paint primer is what I use. Once coated I drill a few holes in it for "grab" and score it up a little and then apply my base material. Because of its smoothness, it accepts paint nice and can be faux painted to look like everything from stone to metal to wood. Its weight makes it an ample base for anything top heavy ike a/c in flight or tall figures. It is also cheap. a 4' x 8' sheet of 3/4 inch mdf will run you about $10-15 depending on your location. Get the guys at home depot to cut it for you if you feel sheepish about doing it yourself. I use the stuff on a pretty regular basis and have never had any real problems with it. If you do cut, machine or sand it, WEAR A DUST MASK. Its pretty noxious in dust form and you'll end up looking like you've been tear gassed. Again use a plywood blade or a rotozip tool. It is available in everything from 1/2" to 1".
Now you know way more than you ever wanted to about wood products. But I figure if you know the mechanics you'll make a better decsion down the road and avoid heartbreak from a damaged or warped base.
Mike