What's on the circuit
Usually lighting circuits are protected by a 15 Ampere breaker. This means that if the total circuit current draw is greater than 15 Amperes, the breaker will trip and open the circuit. It's suggested to only load a circuit to 80% capacity, so the total current draw should only be ~12 Amperes (1440 Watts). The first step in determining if you should add a new receptacle to a circuit, is to determine what's already there and how much power it's sucking. There are many list available online that list the typical wattage of various appliances, that can be used to estimate how much power you're currently using.
Turn off the breaker for the circuit at the main service panel, and make a list of all the items that lost power. Add up the wattage of all the items, and determine if your circuit can handle the load you plan to add.
Electronics and motors don't mix
When motors start (vacuum, circular saw, drill, etc), they draw a large amount of power for a short amount of time. If these items are connected to a circuit that also supplies lights, you may see the lights dim briefly when the motors start. This may or may not be a problem for lights, but you may find that sensitive electronics (TV, computer, etc) don't like it so much.
Blow a fuse, wander through the dark
It's often recommended to keep light circuits separate from other circuits. This is done for the simple fact that if you trip the breaker, it's nice to not be standing in the middle of a pitch black room because of it.
Imagine this
You get your project all ready to be cut, you line the saw up, pull the trigger, and click. You're standing in the dark.
Circular saws tend to be rated 12-15 Amp, which means they'll push most circuits to the limit all by themselves (15A * 120V = 1800W). This is why it's a good idea to not mix lighting and motor loads.
Is the wiring already in place
In some cases, only 2 wires exist at the switch (excluding the equipment grounding conductor). There will be a wire carrying electricity to the switch, and another that carries it to the light when the switch is on (closed). In a situation like this, you'll have to run more wire to connect a receptacle.
In other cases, the power for the circuit passes through the switch box. This is the perfect situation, because you can use the power at the receptacle before interrupting it with the switch. In this situation, you should see 4 wires (2 cables) in the box (not including the equipment grounding conductors, which may or may not be present).
Yes, absolutely!. You can do this by pulling out the switch, and splicing together the two wires that formerly went to the switch. Then put a blank cover plate over that switch's electrical box.
You should know however, that you don't have to have a constant power outlet for a garage door opener. You can have a garage door opener on a switched outlet just fine. And you can use that switch as a lightweight form of security lockout.
I would recommend instead you put a switch guard like this over it, and just keep that switch on forever. It's less work and easier to undo. It also would let you cut power to your opener if you wanted to without getting up on a ladder.
Put a descriptive label on it "Garage door, do not turn off" if you want.
You can also get adapters that give you two outlets and a light socket with a pullchain, into which you can plug your garage door.
This way you can keep the light in place and also avoid having to do any wiring in the ceiling. However, you should shop around and make sure it can supply the amperage you want. Use LED bulbs to conserve amperage and stand up to the vibration of the opener better.
If you cant find a double-outlet-plus-pullchain-light adapter (above) that satisfies your amperage need, then consider one of the single-outlet adapters:
Lastly, if none of those do what you like, you should replace the light fixture with one that has its own built in outlet, so that you don't lose the overhead light capability. This is rated for the full 15A of a normal outlet, and accepts a grounded plug without the cheater adapter you would otherwise need for the light-socket-to-outlet adapters above.
You can get all of these parts at any common home center. Have fun!
Best Answer
It looks like you have a standard box and not a light box. So you don't need the light box receptacle cover. In theory, you should be able to add the receptacle without issue and just use a standard outlet cover.
You can split the hot side by breaking out the tab. Assuming the nutted blacks run to the switch, you can add another hot and wire it to the top "always-on" outlet, and let the switch power the bottom.
The only downside I see to this is they're grounding to the box. Without knowing if the box is grounded, you might not be getting any ground at all if they just screwed it to a wood joist. If the box is grounded, what you'll need is a grounding clip and then run a wire from the clip to the outlet.