Does an unarmed attack always has the improvise quality and that cannot be lost due to paid doom?
Is that also the case if a SC has the unarmed talents and using them? 
Yes, the Improvised quality always applies.
That is why there is the Athletics-based Talent “Brutal Brawler”:
Prerequisite: Pugilist, Athletics Expertise 2, Melee Focus 2
You can ignore the effects of the Improvised quality, and increase the damage of the basic Improvised Attack by +1[CD].
You could - and should - take that, if you want to invest into the Martial Arts Talent tree.
Base Damage becomes 2 + 1 = 3 [CD] (+ Melee damage bonus) and you treat rolled Effects normally, that means, they trigger qualities that are based on Effects rolled and cause +1 point of damage per Effect.
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Thank you. I did not see that talent. So, now its all clear and understanding the unarmed fight mechanic better.