Would I do that? Never!
No Eureka moments while I was away, but CH's comment about Flame Speed could be important here. Air is smaller molecules than methane (I expect!) so comes out of a small hole (pilot jet) much quicker.
I WAS eventually able to get a match to the pilot, by turning the whole burner assembly backwards, so it stuck out into the hall - I though I wrote that before, perhaps it was on the ARGI site.
To begin with there was no reaction, but as the gas concentration in the mix increased, the mixture did light from the match onwards, ie not from the jet, and it didn't stay alight when the match was removed.
SO it may be that the flame speed of the mixture (which would presumably vary with concentration), was too low at low concentrations, to light back to the pilot jet, with the weak mix coming out faster than 100% gas does.
I don't think we can assume anything about the small leak appearing like a semi-permeable membrane between liquids where osmosis happens. The intermolecular forces would be radically different. Molecules in liquids have forces holding them together, in gasses they bounce off each other. I think osmosis still partly applies to gasses but the membrane is not the same as a hole.
In a static situation, I don't think Brownian Motion would provide much of a force for the gas exchange, but the effects of the weather, as I and others suggested, could be quite significant.
Just gut feeling really.
A final thought - if there were TWO tiny leaks, it would be possible for one to let air in and the other if higher, gas out, which provides a force (gravity) for the gas exchange.
I'm feeling too middle aged right now to work out the pressure resulting from a 1 metre height difference - doing it mentally it's 0.05 mbar which isn't much, but it's there.