The tyre pressure won't undergo any significant change. It is dependent on the resistance to expansion of the tyre carcass, not atmospheric pressure.
Tyre carcasses are steel, kevlar, etc, and won't allow any meaningful expansion beyond their recommended inflation pressure.
If the container (tyre) size and the amount of air inside it don't change, then the internal pressure can't change either.
Tyre pressure gauges don't take ambient pressures into account. They are
calibrated to sea-level pressure (or whatever the industry standard allows.)
So no change there either.
At an insignificant level, the carcass will balloon a tiny amount as no material is totally inelastic.
Significant changes to pressure might be caused by extra heat generated as
the bike accellerates and brakes on those mountain slopes or if the air temp
is much lower than below.
So apart from the engine losing a little stomp, the bike would work fine.