* Explorer's Effect: "If this card is Special Summoned, negate the effects of the Special Summoned monster until the end of this turn." This effect applies to the Synchron monster summoned by Explorer, making it unable to use its effects.
* Junk Archer's Effect: "If a Synchro Monster is Special Summoned using this card, negate the effects of all face-up monsters your opponent controls until the end of this turn." This effect triggers after the Synchro Summon is complete.
* Quickdraw Synchron's Effect: "If this card is Special Summoned by the effect of a monster, you can Special Summon 1 Level 1 or lower "Synchron" monster from your hand." This effect cannot activate if the Synchron monster is summoned with its effects negated.
In short:
* Junk Archer can still negate effects because its effect activates after the Synchro Summon.
* Quickdraw Synchron cannot activate its effect because the Summoned Synchron's effects are negated by Explorer's effect.
Therefore, while Junk Archer can be used to negate monsters even when the Synchro Summoned monster's effects are negated, Quickdraw Synchron's effect is unusable in that situation.