"If the PMO doesn't have clear defined objectives right from the beginning, it is doomed to failure." Do you agree and why?

It depends ,,,, If the PMO (or any other function/department as a matter of fact) does not have clearly defined objectives, then the actual performance and its outcomes will be compared against expectations, desires and perceptions.   If these are also low and vaguely defined, then all will be confused and there may be no clear issue here.