Would a small pressure sensor be orientation dependent?
A pressure sensor can be orientation-dependent (and acceleration-dependent too, by the way).  

An practical way to test for orientation dependency is to compare measurements at different orientations: horizontal face up (1g), horizontal face down (-1g), vertical (0g).  If you want to be extra-vigilant, you could repeat these measurements at an elevated temperature.  If the datasheet doesn't mention the orientation dependence, and you don't see significant deviations in your measurements, then you are probably okay.