Is the worshiper's salutation immediately after the second prostration without Tashahhud, after catching the second Rak'ah of the 'Isha prayer in congregation and completing what he missed, considered valid?

What you did is incorrect. The correct approach is to recite the final tashahhud before the salām (after making up what you missed). This is considered a pillar by many scholars. For those who omit it, and a long time passes, their prayer becomes void. Some, however, are of the view that your prayer is sufficient and you should perform the prostration of forgetfulness (sujūd as-sahw). The first opinion is the most preponderant, therefore you must repeat the 'Ishā' prayer. Ibn Taymiyyah, however, is of the opinion that an ignorant person who omits a pillar or a condition is not obliged to repeat the prayer.