Geneious R9 and later should run fine on MacOS High Sierra.
However, the initial release of macOS 10.13 High Sierra includes a bug that prevents display of the menu bar in Java-based applications such as Geneious. This issue only affects users that have their operating system language set to a language other than English.
To restore the menu bar, users will need to go System Preferences -> Language Region and set the primary Preferred language to English.
Hopefully a fix for this issue will be forthcoming with the next High Sierra update.
Note that Geneious R8 and earlier will not work reliably if installed on MacOS High Sierra. See the following post for more information - Geneious-R8-and-earlier-will-not-work-on-MacOS-High-Sierra.