Is it possible that tubes actually get better with age?

No 

One engineer friend of mine questioned this whole subject and so he designed a double-blind test. He put the tubes in identical paper bags in another room. Unbeknownst to us he had placed a mark inside the bags so as to identify the tubes in that bag. He then closed the bags and then another one of us who knew nothing about the markings and only saw absolutely identical bags would go in and take whichever one they wanted. So when they came out no way anyone could know which was which. 

We made the comparison and only after we all had voted was it revealed, we all preferred the tubes that had been opened and allowed to breathe before playing.

MC you kill me.. NO they just wear out, hopefully they sound good ALL the way until they are a nubbin'. I just ran a set of 16 GL into the dirt. 2-5% all that was left in the tank.. They sounded BAD at the end, BUT didn't fail.
Sounded like I had a hoodie pulled over my head listening.

Regards

Yes, as a matter fact tubes do improve with age. But only if they have been cellared and not exposed to high heat. Just don't commit the faux pas of so many novices, tube rolling. Never! In order to fully develop the sound stage and harmonic richness they must be carefully decanted, and allowed to breathe. 

That is what I mean. Like cellared wine. 

Maybe the OP is asking if unused tubes sound better as they age like cellared wines.

Fewer cathode electrons = noise increase.

No! All tubes slowly decline in SQ as cathode emissions decrease. Cathode coatings have a finite amount of electrons.

After 50 hours they get no better.