If using a top quality PSU, the overload protections will kick in before the PSU explodes. You may want to read up on PSU reviews on HardwareSecrets as they are like the only PSU reviewer who had the balls to test overload protections on the PSU. (PSU failures can kill expensive PSU testing equipment, you see.) Do note that HardwareSecrets has not tested new PSUs for over 1 year.
However, low quality PSU brands are known to to label PSUs beyond their designed wattage. For example, check out this Coolmax PSU that is designed by Sirfa as a 600W PSU with 80+ performance but got labelled as a 700W and a 950W PSU by Coolmax.
Coolmax CUG-700B 700 Watt Power Supply Review
Coolmax CUG-950B 950W Review
Even though the components inside can tahan the increase in current if it does not blow up first, you are likely to get out of spec voltage regulation and ripple at wattages that are way above a PSU's designed wattage and this is likely to kill your parts very quickly.
Therefore, please do not attempt to override a PSU's overload protections and overload the PSU in an attempt to save $$$ as you will end up losing more $$$ replacing your dead components.