ANSWER:

Yes, providing there are no things requiring him to be tormented in the grave or punished in Hell! The hadeeth is authentic, and one enters paradise or jahnnam after the Day of Judgement. However, he will enjoy or be tormented in his grave accordingly. Also, the hadeeth talks about the final destination and not necessarily referring to the life of the barzakh.

QUESTION: There is a hadith that states that a perosn who reads ayatul kursi after every fardh salah will go to jannah instantly after death. I assume that means that the stages (questioniing in grave, barzakh and day of judgement) will not exist for this person.