Yes you can hang them on vinyl. Here is a video showing the steps for how to do it!
Though there are a few things to keep in mind:
If your siding has a similar profile to clapboard siding, you'll want to be aware of where you place the mounting piece so that the cleats can slide onto the mounting piece without hitting the siding and prohibiting the cleat from working properly.
The mounting system is similar to a french cleat, so worse case, you can place another small piece of wood behind the mounting cleat to build it out away from the obstructions of the siding. The other thing to keep in mind is that tightening the mounting piece to a part of the unsupported vinyl profile may cause it to deform, so just keep this in mind when finding the right place to attach the mounting piece.
Whatever the material of the wall behind the vinyl, you'll want to be sure that you're adequately penetrating structural material so that the fasteners can support the weight of your BatBnB. If this requires longer fasteners than those included with your BatBnB, we would recommend purchasing the fasteners at the size and type that will work best for the materials of the wall you're mounting to.