Nope. CompositeLab doesn't create effects. It is for compositing elements into a scene. If you have your shot of spidey, and you have a seperate file that is a shot of his web (such as this
), and you want to composite the two together, then CompositeLab is an excellent tool for the job.
If you want to create effects such as Spiderman's web, EffectsLab is a much better tool for that, as it is designed for creating effects. Even so, the success you would have in creating a web is limited, and won't be as simple as two clicks. This type of effect is probably best done in 3D.