Is it necessary to connect relay contact at voltage zero?
Relays are electro-mechanical and dropout time will be in the order of tens of milliseconds or more. If a snubber diode or resistor is use the drop-out time will be longer. In addition, mechanical differences between the contacts of several poles of the relay will mean that the contacts open at different times.
It will not be possible to control the relay to switch off at a specific point in the mains cycle.