I don't think randomDelay is behind this (like 99% sure). First, it'd make no sense to implement it like that instead of just randomly extending startDelay as a value. Second, I took a look and of all the saves I have, mine or others', only the one referenced in my first post and a quick battle save (which is in BattleScape and fakes the mission site anyway) had 'detected: false'. My experience has also been that missions go straight from alienMissions to missionSites in the save, and it's the former that have starting times and are 'placed' at the beginning of the month, and the latter that can be 'undetected'.
Using the same save from the XCF discussion, you can proceed to the site normally and even start the mission while it's 'undetected'. Looks a bit weird when there's no destination marker on the globe, but that's all. Check it out yourself if you wish, a test save is attached.
So, IDK what's going on here and how much of it is intended. It's probably mostly OXC code and not OXCE, though.