How it behaves depends greatly on the plastic, as Gene said. A hole saw will work but may leave the edges a bit ragged. But the pilot drill of the hole saw really wants something more than 1/8 of plastic to keep it centered. If you can clamp a 1/2 piece of plywood to the back side, it will work better. If you can't do that, drill a hole through the plywood first, clamp it to the front side and use it to guide the saw. You will have to be very careful when the saw breaks through. Sometimes it is best to check and stop just short of break through, and finish with a sharp knife. If it is ABS or some kinds of PE plastic, you must run the saw VERY slowly or the plastic will melt onto the saw, makes a mess of the job. I would probably cut it a bit small and then finish out with a Dremel type tool to get better edges more reliably.

There are two other ways (at least) to build the box: One is to construct it from Starboard or other HMPE, either screwing the sides together or using G-Flex to glue it together. If you use G-Flex, follow Gudgeon Bros. instructions for surface prep, particularly "flaming" the glued edges - this is what makes PE glueable. One problem with G-Flex is the yellow color so you want tight joints and clean it up well. 3M 8100 is white and will also work but use the same surface prep regardless of what they say. Another way to make the box is to get some extruded polystyrene foam (styrofoam used for insulation, not "bead board"), carve the shape you want minus the wall thickness, and lay up fiberglass around it as a form. You can make virtually any shape you want that way - nice curves, rounded corners, etc. You must use epoxy with the styrofoam, polyester will melt it. When you have the plug carved, apply aluminum foil to it with spray adhesive - then you can wax it for a mold release. If your shape does not allow the foam to come out, you just chip it apart with a screwdriver or chisel, and pick it out in pieces. Another mold release technique is to cover it in plastic packing tape. You can usually find the blue or pink extruded polystyrene at Home Depot or Lowes, if it isn't thick enough for your form, laminate up a couple of pieces using just about any glue - but softer glue is better (or keep it away from the edges) because it will make a hard spot for your carving and sanding of the plug.

Advantages of Starboard - will last a long time, does not need much finishing or painting, but will look a bit utilitarian. Advantages of fiberglass - will last forever, can be made a pleasing shape, but will require sanding and finishing and will chip like any painted thing.