Yeah it will work but not well. It’s nothing more than a y cable and A small 12volt battery. I tested running the system on a 12v battery I had and I could get it to run but without the 24v power supply connected.
The issue is When you connect your 24v power supply to it. it will try to draw the power down to 12v. That will eventually kill the battery. I also imagine it will also cause other issues.
The best way to fix it is to use a boost converter that steps 12v to 24v from the backup before the y adaptor.
I actually went a different route entirely.
https://www.reef2reef.com/threads/solar-generator-for-backup-power.621771/#post-6227839
Hope this helps you out.