No, I made a much stronger claim. The string that I constructed, 11011100101110111... (concatenating the integers in binary) will contain the works of Shakespeare somewhere within the string. It's constructive.
The way you have described this string it has no length boundary, and thus is infinite. This is the "plenitude" argument Dallaporta speaks to - i.e. everything that can exist, does.
I can see where that leads to multi-verse theory, but what would infinite chance have to do with evolution biology?
Well, wishing does not make it so. I doubt very much that without the aid of a computer either you or I could translate the works of Shakespeare into a binary string in our lifetimes (if nothing else we would probably die of boredom!). However, for such a string to arise at random is utterly impossible. Yes, impossible. To set up a set of rules to create it would be a tremendous task. But again, the problem is not of copying something, it is of creating something. To create one must look forward, one must have insight, one must have intuition, a muse perhaps, things which matter does not have.