In the purist sense of "the electricity I use was actually generated by a wind farm", your idea is broadly correct. However, unless you actually have solar panels or a wind turbine on your house, that's not how the system actually works.
Broadly, all the electricity generators feed into the national grid (which in Australia covers only Qld-NSW-Vic-SA, but that's 90% of the population). From the grid power gets distributed to whoever needs it and there's a lot of fussing to make sure it all works correctly. But one thing that doesn't happen is segregation of renewable energy to renewable energy customers. Then everyone has an electricity meter, and different retails compete to be the one who bills you for what you use. They buy generated electricity and it's metered on the way in, and they have to balance that against the electricity that they sell. It's no more direct than that.
Think of it like a communal water tank - there's a well, some rooftop collection and a creek all feeding into one tank. Then everyone draws water out of it. If you add your rooftop to the collection there will be more rainwater in the tank and less river water, but there's no way for you to draw just rainwater out of it. The electricity grid works the same way.
Then how are you "broadly correct"? What you shifting your electricity demand to daytime does is push up demand during the day, and reduce it during the night. This does mean that you're helping a tiny bit to push demand towards daylight hours, making solar more suitable. Unfortunately, only a tiny bit unless you get a big campaign going so thousands of people do the same thing. Which doesn't mean that it's pointless, any more than any other single action you can do is. Especially since the cost of doing it is pretty low - a small amount of effort on your part. But it's a small step and most electricity still comes from fossil fuels.
But there are better ways.
If you don't have PV panels, the way to make sure you're using renewable energy is to pay for it. Almost everyone in the first world has the option of paying a little extra on their power bill to get renewable electricity. We chose our electricity provider specifically because they have a "100% wind power" option (and they're not one of the awful companies who are busy fracking and starting up mothballed brown coal plants. Ahem). You can do the same. What that means is that for every unit of electricity you use, your retailer buys one unit from a renewable energy provider. The more you use, the more they buy, and overall, the more renewable energy gets generated. I have friends who really do say "I leave the lights on because buy green power, so the more we use the better". Which is not really correct if you're talking about overall environmental impact, because even "green power" takes resources to build and operate. If you do feel like putting money into building more green power, you're better off donating/investing in the companies directly or buying and keeping Renewable Energy Certificates (RECs - assuming you're in Australia).
The other thing you can do, even if you're renting (green renters), is work to reduce your electricity consumption. The lowest impact electricity is the electricity that doesn't get generated in the first place. LED or compact fluorescent light bulbs, when you replace your whitegoods buy for electricity consumption (and turn them off at the wall when not in use), if you have a PVR or computer that's on all the time, again, when replacing it buy for power consumption. If you're not downloading during the day, turn the modem etc off when you go out. Those things all add up, especially the parasitic loads (our washing machine is very low usage when it's washing, but draws 10W if it's turned on at the wall, even when it's "off" at that machine).
In terms of persuading other people to help, you're on the right track - ask people like sustainability.SE for tips, do some research, then focus on things that you know are likely to be effective. If you can persuade people you know to change their behaviour, great (and there are places online to get tips for that). Or join one of the many groups doing that on a larger scale, from local like the Marrickville Green Living Centre to national organisations of local groups like Clean Up Australia (there will be one in your area!) to straight up activist groups like GetUp or research-activist groups like Beyond Zero Emissions