Jokes aside, it can damage not just your system but can be a cause for fire in your house. You could get a much more refined answer if we knew what this bad PSU was and what it was driving...
That Corsair PSU is not meant for dedicated GPUs let alone overclocking. You are risking your whole system by overclocking on that low quality unit. Get something like a Corsair CX550 if you want to overclock. Its a decent quality budget unit.