Wa alaikum salam,
Yes. One can safely say that there is consensus that reward depends on the presence of an intention. The Hadith 'all actions are based on intentions' is only disputed regarding validity of worship not reward. Note the Imam Abu Hanifa makes the intention a requirement in order for an action to be valid as well; however, only that's actions which are considered intrinsically an act of worship such as prayer, fasting, zakat, Hajj, etc... Those actions which are not intrinsically acts of worship but are a means to another act of worship - intention is necessary for reward not validity, such as wudu.
Allah bless you
Yusuf Weltch