The short answer is that it depends on the internal circuitry of the remote. I have a Harbor Breeze fan/light combo that came with a wireless remote, and I know that there are protective circuits inside the receiver that detect if there are non-incandescent bulbs in the system (e.g. CFLs/LEDs, which can cause power spikes, don't work with simple dimmer circuits, etc), or if the wiring is connected incorrectly. This protects against certain short-circuits and against overloading the wiring. From what I know, the basic design assumes you will either use it for a fan only, or a fan with light.
If this is the case, you can't use the remote to control just a light. The receiver will detect that the motor circuit is discontinuous and shut off to protect itself. However, the receiver may not be that "smart", so as long as the Motor Hot wire is capped off to avoid arcing, shorting and electrical fires, the circuit through the Light Hot and Motor/Common Neutral wires should still work. You just have to connect the receiver unit properly; the wires coming out of one side of the receiver should go to the J-box, matching white to white and red or black to red or black, and the wires in the other side should go to the light, again matching white to white and black or red to blue.
If this doesn't work, you're probably going to have to put the light on a wall dimmer. There are models of wall switch that are also receivers for remote controls. Lutron's "Maestro" system uses one wired wall switch, to which a number of wireless controls can be linked and communicate with it via RF. This allows for, for instance, 3-way switching where there used to be none, without having to fish wire. In your case, the Pico remote control works with a Maestro switch and allows similar functionality to what you want with the Harbor Breeze control; a remote you can take in hand and control the lights from anywhere in range of the wall switch. You can get this system at a Home Depot or online. Downside? It's toward the cutting edge of home lighting controls, and so is pretty high-end; the switch and remote control combo is about $80.
The green wire is a ground wire. The purpose of it is to cause the breaker to trip or the fuse to blow if a short circuit develops. The majority of the time you can just hook up the white (neutral) and black or blue wires and never have any problem.
HOWEVER! If a short circuit does develop you may burn the place down!
If you have a metal box connected to metal clad flexible conduit or EMT you should be able to screw a #10 screw into the box and fasten a green wire to it completing a ground. Whatever you have, there should have been a bare copper wire coming in to the box with the black and blue. Some do it yourselfers figure they aren't important and cut them off.
Best Answer
NO!
You cannot, for any reason, connect a grounding conductor to a neutral (grounded) conductor anywhere other than in the service equipment.
If you do so, the metal box and any metal connected to the box (including the fan housing) will become a current carrying conductor. This is very bad, and can result in personal injury and/or death.
I doubt the remote requires the grounding conductor to be connected in order to function.
The device's grounding conductor is a safety feature, and should be left unconnected when installing the device in an ungrounded box where there is no separate grounding wire in the feed cable. However, you'll want to be sure the box is not grounded. Just because there's not a grounding wire in the box, does not mean the box is not grounded. The box could be grounded via conduit, the outer sheath of the cable feeding the box, or some other method.