I upgraded a test environment from 10.6 to 10.6.1 that already had Insights 2.3 and it still works. I created a brand new 10.6.1 environment today and was surprised to find out that 2.3 can't install on it, yet it worked when I upgraded to 10.6.1 and it was already there. So to answer your question, you can go ahead and try to upgrade a test environment without touching Insights to see if it works for you like it did for me, but you'll have to wait until the end of September for the new release if you're having any problems.
Also, you're totally right, all the related documentation I can find doesn't talk about this:
Compatibility with ArcGIS Enterprise—Insights reference | ArcGIS (No column for 10.6.1)
Get started—Insights Get Started | ArcGIS ("you must have a base ArcGIS Enterprise deployment of version 10.5 or later", which is wrong)
I actually have a support case open over a minor display issue I am having with Insights, but the support analyst hasn't told me that Insights 2.3 is incompatible with 10.6.1! Not even Esri support knows, apparently! I'll have to tell him this and close the case...
Anyways, glad I found this forum post! Clearly there was no other way of knowing this. I guess I'll have to wait to give our end users 10.6.1, since they're expecting Insights!