adobe photoshop elements 9/High Sierra

my understanding is that if it worked in 10.12 it should work in 10.13. There are a number of user-to-user compatibility testing sites but like anything and everything on the internet they are not obligated to confirm any claims they want to state. Adobe products can work in OS's they were not designed to and depending on what you do with them your workflow might be fine or it could be severely impacted because you have something you do that the other person didn't need to.

What I've found in support of Adobe products for designers is Photoshop seems to be the least volatile when you run it in an OS it was not tested or supported by Adobe but InDesign and Illustrator can quickly turn into a nightmare.

Adobe says "no, it's not" and they are responsible for their software. Depending on your needs you may be fine using it or you could run into trouble. I would recommend a clean install

According to roaringapps.com Sierra was but there's no data for High Sierra. I'm running Photoshop Elements 2018 so I can't say.