Can air pass through glass?

Yes, but don't hold your breath!
Glass is not a solid, but is a very viscous liquid.  Gaseous molecules
from the air could diffuse through it, given time.  How much time
would depend on the composition of the glass, its thickness, the
particular component of the air you observed (in fact, the glass would
act as a type of filter - "smaller" molecules would pass through first
- you may have yourself a radon filter here!), and the temperature.

MY DAD ONCE TOLD ME THAT THE REASON THAT OLD GLASS WAS VERY DIFFICULT
TO CUT WAS THAT IT IS REALLY SOLID LIQUID. MEASURE THE THICKNESS OF A
SHEET OF GLASS THAT HAS BEEN FITTED UPRIGHT IN ITS FRAME...FOR 20 OR
30 YEARS...WITH A MICROMETER, AND YOU WILL FIND IT IS THICKER AT THE
BASE THAN AT THE TOP. OVER THE YEARS IT HAS ACTUALLY FLOWED DOWNWARDS
WITH THE FORCE OF GRAVITY. GLAZIERS NEVER LIKE TO CUT OLD GLASS. NEW
GLASS IS MUCH EASIER, BEING OF CONSISTENT THICKNESS. HOPE THIS EXTRA
HELPS.

While according to some definitions glass might be considered a
liquid, its rate of flow is insignificant even on geological time
scales. Under most current scientific systems glass is considered an
"amorphic solid" rather than a liquid, which simply means that it is a
solid without a crystalline structure.

Many old buildings do have glass that is thicker on the bottom than at
the top; this is not because of the glass flowing downwards but
because old glass, due to its method of manufacture, was not uniformly
thick. Most glaziers placed the thickest part of the glass towards the
bottom, but careful scrutinizing of old buildings will produce
examples where the thicker part of the glass is at the top, or the
side, or even at a corner if the glass was cut oddly.

According to The Straight Dope, by Cecil Adams, paraphrasing an issue
of Discover Magazine:
(http://www.straightdope.com/classics/a1_120.html)
"Yvonne Stokes, a mathematician at the University of Adelaide in
Australia, says that it would take a mere ten million years for a
windowpane to get 5 percent thicker at the bottom."

Once again: Glass does not flow at any significant rate, including
specifically vis-a-vis the windows of old buildings. Whether this has
any effect on air passing through glass I do not know.

Also see "Glass: Liquid or Solid -- Science vs. an Urban Legend", at
http://www.ualberta.ca/~bderksen/florin.html

Good luck,
Smudgy
Google search terms <glass liquid>

FOR SMUDGY GA

IT IS POSSIBLE THAT WHAT MY OLD DAD TOLD ME WAS WRONG. AND I AM ALWAYS
WILLING TO LISTEN TO MY BETTERS. BUT WHY WOULD GLAZIERS ALWAYS PREFER
TO USE NEW GLASS IN THEIR JOBS IF THE GLASS IS COMING FROM THE FACTORY
WITH INCONSISTENT THICKNESS. MAYBE A QUALIFIED GLAZIER COULD SUPPLY AN
ANSWER. I`M LEARNING ALL THE TIME.