I'm not completely sure I understood the question completely, but here goes:
If the centre of mass of the block is not above the contact area between the block and the table, it will start to move (fall over completely if there is nothing else that stops it). This happens whether there is friction or not.
Ah, I meant that either the centre of gravity is "above the contact area", or to the side of it. Not under it :-) If it is to the side of the area of contact, then you can prove that it starts to rotate to the side by considering the torque of gravity upon the object, with respect to some appropriately chosen axis.