If so, what you propose won't work for a couple of reasons. First, you're flipping the plate, which means left-right or top-bottom is going to get flipped. Second, with a single laser you'll be illuminating one version as a transmission hologram, and the other as a reflection hologram. That's not going to work, I'm pretty sure.
Another way to attempt to do what you describe is to use two lasers to illuminate the same hologram: one, say, at 45 degrees to the plate coming from one direction, and the other 180 degrees opposite, shining on the plate from the other direction. If the two beams mimic the original reference source (but with one being the perfect conjugate: same angle but opposite direction), you'll get both a real and a virtual image.
However, and this is the big however, the hologram "knows" only about light from the parts of the object that are visible to it at exposure time, and it faithfully images them back into space exactly where they were. That means that the real or projected image will be pseudoscopic. It will be viewed from behind it's original location and will appear inside out or depth-reversed.
An interesting effect, but probably not what you were looking for.
Breaking the plate in half isn't like cloning the hologram, although it's a common myth. Imagine a hologram like an ordinary window. If you look through it, you can see objects on the other side from many different perspectives. Now cover up half the window. You can still see many of the same objects, but from a restricted range of views. And if a fly was climbing up one side of the window, you probably can't see the fly from the uncovered piece: the optical information about the fly is gone. To clone a hologram, you can either recreate the interference pattern (e.g., stamped foil holograms from a master) or reconstruct the original image optically and make a new hologram of the original. Rainbow or "Benton" holograms use this technique (can be used for both techniques, actually).
Hope that helps.