if it a good power supply with over load protection the unit wont turn on..or your rig will turn on fans but not post or under large load it turn off. if it a cheap unit most times if the power supply is over loaded it pops and dies. if your lucky when it pops that it does not kill other parts. why dont you post your spec here and we can tell you if your ok???
At best, errors, bluescreens, lockups, or it may not boot at all. At worst, as stated, cracks and pops, smoke, fire, damage to other hardware in your system.