Does a long flight on a jet provide a headstart to altitude acclimatisation?

I'm pretty sure the effect can be neglected for passengers.

The first reaction of the human body to lower air pressure is deeper, faster breathing and a higher heart rate. On the other side, passengers are only sitting around, doing quite nothing. This leads to lower heart rate and slower breathing. Putting both together, passengers breathe a little faster than normal when sitting, but not heavy, and the body does not really encounter a lack of oxygen. There's simply no trigger for any acclimatisation.

Even if, the body mainly reacts by producing more red blood cells. This takes many days to weeks, and even an 18h flight would not be enough.

Finally, typical cabin pressure corresponds to altitudes in the region of 2000m and below, which is not that high.

So there should be no effect on the passengers, and may be a little effect on the flight attendants.

Not really, the effect is neglectable. There are two main reasons:

• The altitude is not high enough. Typically the cabin is pressurised to an altitude in the range of 1500-2000 meters (source and matches with what I measured with an altimeter during flights). In that range the need for acclimatisation is not very big, unless you would like to perform competitively in sports at that altitude.
• The time is too short. Even flights across the Pacific will be something like 12h. Such a short time is rather irrelevant, especially if you land and spend time at a lower altitude after the flight.

According to me, any positive acclimatisation effects will be offset by the negative effects of spending all that time in an uncomfortable position with a lack of movement.

Does it contribute, yes. Will the difference be noticeable, no.

Proper acclimatization requires you to spend several days at each of several intermediate altitudes before reaching your target altitude. That is why climbing expeditions walk in and then set up several climbing camps working their way up the mountain. They get used to each higher level for several days before moving to the next higher.

If you are hopping a plane from Sydney to Kathmandu, then those hours count towards getting used to Kathmandu's altitude, but contribute nothing really towards acclimatizing for Namche Bazaar. Of course that assumes you fly to Kathmandu, if you stop off in Bangkok for a few days before heading to KTM the slight gain is lost.

Bottom line there is no real short cut to acclimatization, it takes time, from a few days to a month or more. Each person reacts differently to altitude, so there is no magic bullet that works for all. Best bet is to build the necessary time into your plans or bring medicines to help ease the altitude issues (or both).