Yeah, bring all the parts and tools you can think of in your checked luggage. Include a pump, and practice using it before leaving home.
A new chain is seldom needed, so you might skip that.
When picking up a new cheapo bike, inspect...
Chain tension if 1-speed or hub gear
Handlebar fastening – both bolts
Wheel bearing adjustment
Crank and steering adjustment also, I suppose
Cheap bikes often come with no grease in bearings
Spoke tension, but that requires expertise.
If you have a chance, I suggest replacing the original inner-tubes with Thorn Resistant ones. It is not that there are thorns on Playa, but the Thorn Resistant tubes are soooooo much more resistant to all punctures. They also hold air pressure much better, keeping you from riding on under-inflated tires after a few days.