Fascinating question! I think they *may* do – as one of the ways that the body responds to being at high altitude where there is less oxygen. However, one thing I am more certain about is that they will have higher levels of a molecule known as bisphosphoglyverate (BPG) in their blood. BPG can stick to haemoglobin and changes its affinity for oxygen – if BPG levels rise, your haemoglobin is better at binding oxygen and allows your blood to grab more oxygen from the air in your lungs.
People wanting to climb high mountains need to spend a few days at high altitude before making their final assault on the summit – in order to ‘acclimatise’. What is happening during this period is that the body is making more BPG which increases the oxygen affinity of haemoglobin and allows you to survive.
Thinking about it a bit more, there may be less of a change in pilots since the interior of an airplane is pressurised – the atmosphere is more like what you have at ground level, even if the plane is high up.
Thanks for asking this question – learning about the intricate mechanisms of oxygen binding by haemoglobin (which were revealed by protein crystallography done by a hero of mine – Max Perutz) was what inspired me to get into kind of research!