There are a few common failure modes to aluminum electrolytic capacitors. Heat buildup, over current, age breaking down seals, and poor quality are some of the modes most of us have experienced. That said, there is one failure mode that's not so obvious, and keeping a capacitor in a cool dry place can extend the amount of time it will survive, but all AEC's will break down over time.
Here's where we get into the complexity of how aluminum electrolytic capacitors work. I'll keep it over-simple. AEC's are made by wrapping conductive aluminum layers with an insulator and saturating them with an electrolyte. Once they are made, a dielectric aluminum oxide layer is formed via a dc current flowing through a limiting resistor. In order for this layer to not break down, the capacitor has to be used. If not, and over time, the oxide layer will break down and the cap will fail. That's why capacitors often list a shelf life in the data sheet. When the oxide layer breaks down, it can sometimes be reformed the same way it originally was created, though you would need to remove the capacitor from the circuit it's in before it could be done. In the end, and other complexities aside, it's far easier to just get a new cap.
So, will a sealed board last longer than one that's in a computer? Answer: Depends. Assuming all capacitors are the same, if your board is in a climate controlled place and sealed in a dry bag, then it will probably last longer than one that is exposed to humidity but otherwise stored in the same temperature. Breakdown times are also influenced by the quality, chemical and physical properties of the cap, so it's near impossible to accurately predict how long one will last.
Though in the end... entropy *always* wins.