They can, however as missions and events are generated at the beginning of the month, the reload also has to happen to just before the start of the month.
Thanks for tip! Now I see it. So as rule of thumb keypoint saves should be made only at the end month. Alas, I have been doing the opposite until now.
It's hard to give more specific advice without more details, but saves are human-readable, so you can peek inside and try to make your life a little easier.
Yes, and I have a decision now (1st july, after positive ranking, but already heavily undermined by mod design & rng) - reload this game from previous manual save (1st june) and abandon quite good month, or cheat (wipe) savefile heavily and have just an empty month of alien activity, because it was really... active here.