I would think the plane is safe and perhaps the plane could be considered as territory of the nation of the diplomat therefore the diplomat could offer him asylum on the plane if need be, but I may be wrong about the latter.
(Source: I used to have diplomatic immunity.)
I do not have direct knowledge, but I would think that if the plane is of the diplomat, then the whole plane could be considered to be territory of the nation of the diplomat, therefore the diplomat could offer him asylum while on the plane.
If I wasn't clear, I was not speaking about offering him diplomatic immunity, but rather the plane being considered as territory of the nation of the diplomat.
Somewhat more seriously, pretty much the only perk was getting to use the Diplomats & Crew line at airport immigration. Most countries, including mine, make their diplomats pay their parking fines etc, and while I was theoretically exempted from security checks, it was virtually always faster to put your bags through the X-ray and walk through the metal detector than it was to pull rank and wait forever as the proto-TSA at the time ran around like headless chickens, looking for the manager's manager's manager needed to authorize the exception. The police treat diplomats with either thinly disguised contempt (if they ran into them a lot and knew they couldn't do much of anything) or, more commonly, puzzlement; and once again, it was usually way easier to pop the trunk and let them have a look than it is to invoke immunity and deal with the resulting confusion.
And as far as complimentary upgrades to first class and "ambassador's lounges" (wot?) do, I'm not sure what the other reply has been smoking, but it's probably not the Vienna Convention. Airlines don't give any free benefits to diplomats, they earn their status through butt-in-seat miles like the rest of us.