I’m not sure if this is possible, so apologies if not!
The larger problem is that when I do a global search for something, I often get false hits from the .sfdx/orgs directory, when I actually wanted to just search all of my source. I can add the .sfdx/orgs to the excluded list on a per-project basis, which solves that.
But, there’s no global setting for that in IntelliJ (see https://youtrack.jetbrains.com/issue/IDEA-150784). So I have to do this for every single project.
I think the IC plugin probably generates the .idea/My-Project.iml so you might be able to do this for us in SFDX projects. I can’t see why anyone would object, and they can always remove the exclusion if they prefer.