Yes, Geneious does run on El Capitan.
There is one issue users need to be aware of when upgrading to R9 on this OS. Geneious R9 is bundled with Java 8, and when this version is installed by overwriting earlier versions of Geneious running with Java 6 (eg. by dragging it to the Applications folder and choosing to replace), Mac OS will no longer let you run it, stating that the app is "damaged" and should be moved to the trash. The easiest fix for this is to restart the computer and it will stop happening. Alternatively you can rename the Geneious app to anything else and it will stop. This appears to be due to a bug in Gatekeeper, the security system on Mac OS.
Note, Geneious R6, R7 and R8 use Java 6 on Macs, which may not be installed by default on El Capitan. If this is not installed, you will need to download and install the latest update for Java 6 from Apple (1.6.0_65). You can download this from http://support.apple.com/kb/DL1572.