Most destinations are in system, some are 1 jump away, rarely 2, very rarely 3, extremely rarely 4 (if I remember correctly). I don’t think I’ve seen further than that. Maybe 5 but it would have to have been exceedingly rare. Might as well buy a lottery ticket at that point.
Using existing mission location mechanics, I see no reason why trig invasion systems should be treated differently. (I’m not saying I agree with this - I’m not fond of how Invasions are implemented at all.) To be clear, I have never personally seen an empire space agent send you to nullsec and I doubt that would ever happen (there are some NS systems directly adjacent to some HS systems), but I don’t see why an empire space agent shouldn’t send you to fake lowsec. I doubt that they send you to fake nullsec - none of the United Standings Improvement Agency [USIA] runners have reported that ever happening (they are paid handsomely to run missions and have been for the past 11 years). As for destinations that pass THROUGH these systems… well, that was already a thing before Invasions; there were already destinations such that no HS route existed, and Invasions haven’t changed that fact.
CCP has provided zero indication as to what permanent mechanics will be for Invasions and flipped systems after Chapter 3 ends, so this discussion would probably be best put on hold until that is over. Don’t be surprised if the agents themselves relocate to new stations outside of trig systems and if the trig systems themselves are no longer directly accessible via stargates (T-space FTW) - lorewise, agents have the capability to relocate as human beings.