Greenboard drywall is a moisture-resistant type of drywall. The actual interior of the board is the same as any other type of drywall, but the face is made up of a moisture-resistant material that is useful in areas where water or moisture occurs over time. However, greenboard drywall is not waterproof, which means it is not an acceptable substrate to use in areas with extreme moisture.
The level of exposure you expect will determine whether or not you can use greenboard as an acceptable backer board for tile or not. If you are looking at a commercial kitchen where excessive moisture and daily soaking of the backsplash and areas around it are a normal part of the routine, then greenboard will not be an acceptable material because excessive levels of moisture will eventually soak through the face and rot the board.
The average kitchen offers very little in the way of water exposure to the backsplash. Washing dishes in the sink rarely creates much more than simple over-spray, which generally dries off of the face of the tile and grout long before it has a chance to soak through the grout and affect the backer behind the tile. As such, greenboard is a perfectly acceptable substrate for the average kitchen where only normal moisture levels over time are expected.
If you are planning on sealing your tile installation after it has been installed on the backsplash, greenboard is no different than the actual sealer coat in the sense that it is just another layer of protection. You can never go wrong with too much protection, but it is also not a necessity for backsplashes where you are already planning on applying a topical coat of water sealing.