Is there any way to convert a semi transparent object to a vector using live trace or any other feature in Illustrator? (For instance, a simple cloud)
Personally I am against live-trace.
Why? — It's lazy and, in mu opinion, completely unprofessional. You can create way better effects and greater quality if you do it yourself (''by hand''). Yes, it is way more time consuming, but you add your own touch to the picture and fix errors it has while doing it.
Another plus is you may encounter something you never knew how to do and learn in the process and end up gaining much more than being lazy and just live tracing something.
I couldn't find a way to do this with Illustrator, but Flash Pro's bitmap tracing (Modify > Bitmap > Trace Bitmap) does handle images with multiple levels of transparency. It only has 4 options (color threshold, minimum area, corner threshold and curve fit) and doesn't always seem to get the colors right, but it will give you a place to start from.
I also prefer Flash's vector drawing tools and shape optimization to Illustrator's. They're simpler, but I find them more intuitive and easier to use.
You're best bet is to make the image opaque via Photoshop or some other Raster app. Then place and Live Trace with AI. Then set the opacity how you want it.
If you mean an image which varies levels of opacity within itself, you could use the raster image as an opacity mask rather than trying to trace it.
A transparent PNG image:
Then a red rectangle created in Illustrator. File > Place used to place the transparent png. Select both the png and the rectangle and choose Make Opacity Mask from the Transparency Panel menu.