If - but only if - the PSU's first step is a regular diode based rectifier, in theory it should not put more stress to the diode bridge nor the following capacitor(s).
However, there may be a noise filter in front of the rectifier that may not work optimal.
Those question we don not the answer to without reading the PSU repair manual / schematic.
Another stressing factor is that using the PSU like that, even if there are no technical reason to think it won't work, I'd assume warranty get broken.
All the above statements and question assume output voltage are pure sinus and it can keep voltage stable all the way from zero to maximum load.
Then you need to know some properties of the inverter:
- How does the output curve looks like? If something else (e.g. square curve form) then that can potentially kill the PSU quite quickly.
- Are the voltage output stable? If not, then the PSU will have a harder job keeping the voltage stable and the voltage from the solar inverter may even start to resonate.
- You say Peak system load 660W. But can the batteries deliver that much of power? Will ther be times of day when the batteries are less full and therefore the peak load getting way less than this. And what is the excact behaviour when the peak load occurs. Does it cut? Does it try to feed voltage immediately again? Will it tend to oscillate between on/off state?
In order to tell if it is safe, we need to know a lot more about the solar inverter AND the atx power supply and at least schematic of primary side / before the rectifier.
The conclusion therefore are : Since we do know about nothing about the solar inverter, then my take on this by now is that it is not safe.