Can a pet rat live on its own?

Well no pet should be left unattended for a long time, although rats are pretty independant. As long as they have a large supply of food and a large supply of water (depending how many rats you have).

I say I dont think anything bad would happen if you left them for a weekend.

But you'd really have to over stuff their cage with food, there is never too much really. But too little can be a harm.