You'd probably need to make sure you're careful to keep the outputs from the two power supplies isolated. Moreover, the inverter powered ATX supply might have a floating ground that could lead to some nasty (and potentially dangerous) situations.
You can use the Opus to trigger the second supply but not quite like you stated. ATX power supply turn on leads (PSON) are active low signals. Thus the line needs to be pulled down to ground to turn on the supply. You can use a relay and diode to do this for you. Alternatively you could use the same solution to power on the inverter instead of the standard PSU. In that case, you'd just hardwire the PSON signal to ground. In this way your Opus would manage the sequencing of your inverter.
If you just want to use the Opus for sequencing only (i.e. no power), then there are probably cheaper solutions. Consider one of the startup/shutdown controllers mentioned in the forums. They provide most of the same capabilities of the Opus (and a few extras) without the hefty Opus price tag.