As long as the overall weight of the bike and box doesn't exceed whatever their weight limit is, you can put panniers in the bike box. I've done it several times and never had a problem. They're not going to open the box to check. It will be x-rayed by security but they don't care whether you have anything in the box apart from the bike.
Deflating tyres is a somewhat pointless exercise. The baggage hold is also pressurised, and even it it wasn't, the air pressure at 30,000ft is about a quarter of an atmosphere so tyres only have to cope with an extra 10 psi or so.
You don't actually need a box, turning the handlebars and removing the pedals is enough - some people say that's better than a box as the baggage handlers can see its a bike and take more care of it than a box.