Agreed it will shut down, while it struggles to provide the power it will become dirty. The dirty power is what will kill your components. By the way, in case you didn't understand it in the first place, the dirty power will damage your HDs, mobo regulators... need I go on.
I haven't even looked close enough to give you the answer in your specific, but if you are questioning it, then consider a new PSU.
Oh never mind, yeah run your existing PSU... It will all be OK. Do you feel better now?
You can't run a medium duty PSU to it's limits without problems.
Understand I Haven't determined your load, obviously.
I have given you the understanding that you already had.