That article is interesting, but I don't see that it addresses the original question.
As far as I know, the runtime size of String objects is only limited by the length field, which is an int.
The soul is dyed the color of its thoughts. Think only on those things that are in line with your principles and can bear the light of day. The content of your character is your choice. Day by day, what you do is who you become. Your integrity is your destiny - it is the light that guides your way. - Heraclitus
I might add to Ilja's comment that you are likely to see OutOfMemoryException before you can use the String approaching the int maximum size. Internally, the Strings are stored as arrays of chars, so even if one char is just one byte, and your machine memory is 1Gb, then the String of size 1 billion is your limit.