Yes, you can definitely spray paint wood as long as it is untreated, with no sealant or varnish. If the wood has been previously painted or sealed, then sanding or priming would be necessary in order for the spray paint to stick to the wood.
Wood is very porous, so you may find that a lot of the paint gets absorbed by the wood even with several coats. Depending on the item you will be painting, whether it will be inside or outside, the type of spray paint matters. Water-based spray paint can give you very good coverage quickly, while an oil-based would be better for wood that will be outdoors exposed to more moisture.
Even without sealant or varnish, it is important to clean the surface before spray painting wood. As with any spray painting job, to avoid dripping, you should apply thin coats and allow the surface to dry completely before applying a second coat.