It's never a good idea to push a PSU out of spec. They're designed to deliver a certain amount of power, and good units will be tested under a range of conditions to ensure they can reliable delivery nice stable power at within their rated conditions. Push them beyond their limits and bad things can happen. Good quality units have a range of safety features which *should* kick in to prevent damage to the PSU itself or components connected to them. They do that by simply hard powering themselves down (like turning the power off to your PC) to prevent damage. If those safety features don't work, or in the case of cheaper/poorly designed units where those safety features don't exist or aren't properly designed, anything can happen. Once components in the unit are pushed too hard they will fail. At best the PSU itself can just self-destruct. At worst they can fail with a power spike that can fry any components they are connected to, or even spark/smoke/flame.
FYI - you need enough power, but every bit as important is getting a decent PSU. Many, many units outright lie about their rated power. Why don't you post your build and your region and we can suggest you a good quality unit that won't cost the earth.