Making a small drain/vent/hole in a glass box
While I cannot cite any specific sources for this, I'm going to posit the following answer:

Yes, structural integrity will be affected, but not enough to be concerned about.

The box you describe is not suitable for carrying any kind of load anyway, and as you state above it's for display purposes.  Drilling a tiny hole will not cause any cracking - in fact it's a technique used in windshields (particularly aviation windshields used in small planes) to STOP cracks from continuing to spread.  (Small hole drilled right at the leading edge of an expanding crack relieves the stresses in a sound manner)

Granted aviation glass is different than what you've got but still - I think you're fine.  I'm curious though why drill a hole in it?  That will have a tendency to trap moisture.