ATX power supply safe on
The described circuit should not work as the sequencing is backwards.

From this Wiki page:


  The ATX specification defines the Power-Good signal as a +5 volt (V)
  signal generated in the power supply when it has passed its internal
  self-tests and the outputs have stabilized. This normally takes
  between 0.1 and 0.5 seconds after the power supply is switched on. The
  signal is then sent to the motherboard, where it is received by the
  processor timer chip that controls the reset line to the processor.


So basically, the sequence would be as follows:


Ground the PS_ON signal to enable the power supply - the PSU sits in standby mode supplying only +5VSB until this signal is pulled low.
Hold all circuitry in a reset state while the POWER_GOOD signal is low.
Once POWER_GOOD asserts (goes to +5V), release your circuitry (e.g. any MCUs, etc.) from reset.


This extra period is specified to allow the power supply rails to stabilise and reach the correct voltage before you start running any processors.



The +5VSB rail is supplied specifically for the reason you suggest. It is there to power things like the RTC (so as no to drain the battery) and also any control circuitry which switches on the power supply. The PSU will specify how much current you can draw, but it is usually in the order of 500mA or so. Powering an ATTiny from this would not be an issue at all.