Can I translate a Shape Dataset more than 2Gb in size

A) There's several reasons why translating large datasets to/from Shape causes a problem...

A limitation of the operating system and system architecture. Internal pointers between the shape file index (shx) and shape file data (shp) are stored as signed 32 bit integers, which cap them at 2GB. (Granted, these are indexes measured in words, so we should be okay to 4GB BUT on some 32 bit operating systems there isn't a way to jump to a location in a file > 2GB from the beginning)
DBF files have a 2GB size limit. Nothing can be done about that (other than to reduce the size or # of columns, if you must keep all your records).
The Shape header has information on the size of the file. This info is held as a signed integer meaning we can't write a Shape dataset >2Gb because the header would be incorrect.

If you have a source Shape Dataset that is more than 2GB it is not a valid Dataset and probably wasn't created with ESRI software.

Note: At the current time FME will produce such large files, which FME (after build 5187) can read back.

A) In a word - No.

A) Same problem. In fact it is often the DBF part that is the issue. See second point in answer of first question.