Can I complete quest components without signing up for them?
Overall, no.
In quests you have to explicitly accept, the "kill counter" doesn't start ticking until and unless you've accepted the quest, and the fifty VENOM agents you already incapacitated won't count toward the fifteen that your contact wants you to take out.
On the other hand, "automatic" quests are added to your quest list the moment you pass through the area they're in so your kills start counting right away.