Yes, HADJ is a Scrabble word!

Letter values in Scrabble US: H 4, A 1, D 2, J 8.

Is it a valid word?

HADJ is a valid word in the official Scrabble dictionary (US), the UK Scrabble Dictionary and Words with Friends (ENABLE).

the fifth pillar of Islam is a pilgrimage to Mecca during the month of Dhu al-Hijja; at least once in a lifetime a Muslim is expected to make a religious journey to Mecca and the Kaaba