Will this HDR trick work? Can somebody confirm?

I have a Nikon D3100 which does not have automatic bracketing exposure feature. So I decided to take 3 shots of a scene with low, mid & high exposure modes and then combine it for HDR effect. Though I used my tripod, there were slight variations in all the 3 pics because of having to change the shutter speed for different exposures.
Now, I have a random thought of taking just one pic and then edit it in light-room to produce 3 different pictures of different exposures and then finally combine them for HDR effect.Is this a good idea? Has someone tried this?

Kind of. You're not going to get anything that you couldn't get by simply using Curves.
What bracketing gets you is actual information in the shadows and light areas that the HDR process can show in variable degrees.

Timothy S basically answered your question, use levels (curves) to bend the contrast curves. That's not HDR.

To do HDR properly, you need something to align the image stack. Hugin, a panorama stitcher, has a nice standalone program called align_image_stack which will make slight adjustments to your stack. Align_image_stack is command line and a great way to align image stacks for further processing in some other HDR program.

Hugin is also capable of doing HDR and aligning the image stack using their normal pano tools to align and enfuse to do the HDR. Enfuse gives a realistic looking HDR, unlike others that give weird colors.

I've done what you mention: take one single shot and then upload it three times into Photomatix. The program will automatically recognise that the pictures are all at the same exposure values, and will offer to create a bracketed set and then go ahead with HDR processing. It looked fine to me, although hardcore HDR enthusiasts may still insist you have to use three (or five, or however many) pictures which were bracketed in the camera.

It's certainly worth a go, costs nothing, and you might like the result.