Can pumps fail due to age? I have a small cache of the now-discontinued Quickex Quicker Pro mini pumps. They have 105 cm3 stroke volume, and 5 kgf force required for 7 bar pressure. In about 100 strokes, I reach 7 bar on 28mm 700C tires. The reason for these extraordinary specs is that the pump has a multi chamber double action design: it pumps even on the outstroke. I am not aware of any other pump with comparable specs. Typical mini pumps require 200-300 strokes for 7 bar, and a large pump such as Silca Impero requires 20 kgf force for 7 bar pressure.
I'm worried that the pumps in the small cache could fail over time due to natural degradation of materials. I store the pumps indoors shielded from sunlight. If all of the pumps in the cache fail due to natural degradation of materials, I'm left with no working pump and no possibility to purchase a pump having similar specs, because no other mini pump manufacturer has realized how to build a mini pump that pumps a tire quickly in few strokes with little force.
Is my worry justified? Can a pump that is not being actively used fail?
Due to their complex construction, it may not be feasible to disassemble and repair a failed pump.
Can a pump that is not being actively used fail?

On the one hand - nothing lasts forever.
On the other hand - you don't need your cache of pumps to last forever. You only need your cache to last:

Until you stop riding
Until you find something else that works as well or better

So, let's say best case scenario, you need your cache of pumps to last 40 years (just picking a number).
Let's also say that you have enough pumps in your cache to last the 40 years (or whatever number you pick) due to normal wear. For example, if one pump wears out every five years you have 8 pumps.
Your question is - will that last pump still work 35 years from now when you pick it up having never been used before?
My bet (in the absence of actual data, which would take longer than I'm willing to wait) is yes, that 8th pump will still work.
Here's why
Your cache of pumps have two things going for them:

The seals are covered with a lubricant that protects them from oxidation
The seals and the lubricant are in a sealed environment

It may be that your real problem 35 years from now will be the oxidation of the lubricant rather than the oxidation of the seal.

Oxidation is the most predominant reaction of a lubricant in service. It is responsible for numerous lubricant problems - including viscosity increase, varnish, sludge and sediment formation, …
Oxidation - The Lubricant's Nemesis

You can increase the odds of in your favor by:

Storing the pumps in a temperature stable environment, as you describe in your question.
Re-lubricating the unused pumps after some period of time (check them at 5 years and set a schedule based on your observation) would assure that the lubrication does not break down and gum up the pump. Re-lubricate the pump with a lubricant that is similar as possible to what you find in the pump.