Does variations in air pressure affect the melting point of PLA and ABS while 3D Printing?
Boyle's law refers to properties of an idealized gas, where the product of pressure and volume remains constant.  Taking into account your description, as well from filament-based 3D printers seen so far, my answer is no, Boyle's law does not apply here.

If running by extrusion, polylactic acid (PLA) is heated to overpass melt, however this liquid is not heated to become a gas. Temperature control clearly is of importance, because the viscosity of the polymer depends on it.  And viscosity co-influences the precision of details you may print, actually down to the scale of less as a tenth of a millimetre.  Without experience to run one 3D print in at sea level, and the same again during an intercontinental flight, I assume it is more likely, machine control takes into account the pressure difference between ambient air and polymer melt, and not (yet) the (in comparison) lesser variations of air pressure.

The chemical structure of PLA shown in Wikipedia's article shows a relatively low number of functional groups susceptible to water, relatively low to the inner backbone of the polymer (in the structural scheme, this is written in the square brackets).  The article refers to typical molecular weights of 130 kDa when PLA is produced.  These two let me say, humidity does not play an important role.