NO it doesn't.
"A spell's duration is the length of time the spell persists." (PHB p.203) there is no mention of any dependency on the flow of time experienced by the caster or the target or anyone or anything else. This means that, unless stated otherwise in a specific case, it is independent.
The spell states (PHB p.274): "it [the creature] falls into a state of suspended animation. Time ceases to flow for it, and it doesn’t grow older". It is only for the creature itself that time ceases to flow. Also note that this is only a clause for a creature, not for an object, which implies the intent is that this is merely so a creature does not age and can be sequestered for thousands of years
It is clear that modifying the duration of a spell is very significant in terms of balance and the ability to do so is extremely limited. The sorcerer metamagic Extend Spell ability is one of the very, very few examples in the game. From this it can be inferred that the intent of the rules is to avoid things that modify spell durations. So if there is a rules call or interpretation to be made we should err on the side of spell durations not being modified
Even without these general points the conjured creatures are not sequestered, the magic once cast is "external" to the caster so would not be within the sequester effect in any case
Most conjurations generally require concentration. Conjure Fey, for example, has a duration of "Concentration, up to 1 hour" (PHB p.226) and as a DM I would rule that being in suspended animation means you lose concentration
All this adds up to a no.
A related question: what happens if you sequester a conjured creature/object which has an applied spell duration?