Continuous effects never take place in a Chain Link. It is only when the card is actually played, that it would be a part of a Chain Link.
Unfortunately, that is not how it works, as it's been ruled so. Dark Armed Dragon and other monsters of the like can only be special summoned on their own terms, from the hand. You cannot use cards such as Monster Reborn to special summon it. It is an illegal play.
Source. It can also be found on Netrep.
Fair warning; I am the last person you should be wanting to question rulings with.