Custom triggers are not explicitly documented or certified in ArcGIS software but we do provide some guidance about what tables can be edited and which cannot: What type of data can be edited using SQL?—Help | ArcGIS Desktop
Triggers can cause some unintended errors or issues in ArcGIS software which can be difficult to identify and resolve. That is not to say it's impossible to implement them, some customers have successfully implemented custom triggers in their deployments, but it requires a lot of testing to make sure ArcGIS workflows are not impacted negatively.
On a related note, Esri Technical Support will ask you to remove any custom triggers before beginning troubleshooting. However, we do have a number of out-of-the-box solutions or tools that may be able to accomplish the same workflows you are looking for in a trigger.
