Exceeding the relay contact rating and connecting to Arduino
No you cannot. The principal failure mode of relays in over-voltage conditions is arcing between the contacts on switch off. It doesn't matter how long the relay has been on, exceeded voltage rating will prevent it from cutting the arc off fast enough. If anything, switching it on and off repeatedly will only kill it faster.

A faulty relay connected to mains voltage can easily catch fire or explode and project molten metal particles to your face (or silently die - don't take this as a recipe for pyrotechnical show). So I'm inclined to say there is a danger.

EDIT: to make my point crystal-clear, once the relay is switched on, it doesn't care about voltage anymore as long as its current rating is respected. It will not heat up or otherwise suffer from over-voltage, since the voltage drop on closed relay contacts is close to zero. You could apply literally millions of Volts to your circuit, and practically all the voltage would be dropped on the load (provided it can cope with millions of Volts). The moment you try to switch the relay off however, it will see the full voltage applied on its contacts, and fail if its spec is exceeded.