I think someone many moons ago had this strange idea that they would explode if still pumped-up because the aircraft hold is unpressurised (which they were on older aircraft - modern ones may be presurised the same as the cabin - say 8000ft).
But assuming your tyres were inflated to 90PSI (say), that's 4 atmospheres (well, 4-and-a-bit, but...).
And assume air pressure on the ground is 1atm
If there were absolutely no pressurisation in the hold (there is a bit even at 36000ft) that's only the equivalent to your tyres being inflated to 5atm, or 105 PSI
Which will be well within safety limits for the tubes, tyres & rims, so yes they're highly unlikely to explode.
No more so than the aerosol cans of shaving foam, hairspray, etc which people are allowed to put in their luggage.
As User says, deflate em and you'll just have to pump em up again at the other end.
And having air in the tyres will help protect the rims if your bike is knocked-about (if
) by the baggage handlers.