Can flight crew book tickets for themselves, on the same flight?
Since the pilot won't check-in their flight bag, the booking will be cancelled (no-show).
They won't board with the passengers, so they won't be counted, same end result. Answer is no.
Many airlines now prohibit active duty (including relief) flight-crew from mingling with the passengers. Long gone are the days of the pilot walking up and down the plane.
That would be the most expensive shower in the history of showers. A first-class Emirates long haul flight is easily $24,000 (SFO-DXB).
Crew rest areas are beds for a reason, a shower goes against the idea of sleeping (may not be a universal thing though). But I wouldn't want to see my flight-crew in a robe going to bed after a nice warm shower. Unless the robe comes with epaulets.