No, CAT 2013 will not be held online.
CAT is a computer-based test and not an online exam. A computer based test is one which candidates are required to read the questions on a computer terminal and mark the answer by clicking on the right option using a mouse. It is similar to paper-based test except that instead of paper and pen, computer screen and mouse are used.
Candidates are requested not to confuse it with an online test, as the online test is conducted on a particular Internet site that can be accessed from any system.