Wa alaikumu-salaam
The Prophet (s) used to recite the Quran once in Ramadan during the nights with the angel Jibreel but it is not mentioned to be in Taraweeh though.
Therefore, it may be said that is Sunnah to recite the Quran at least once in Ramadan at any time during the day and night. As for taraweeh, it is not necessarily a Sunnah to recite the whole Quran once in it during Ramadan. You may read in
www.islamqa.com for more on this topic along these lines.
Wassalamualaikum