I think that the person can claim the Pre-EMI payed for the house even if the construction does not fall under present financial year. However the Pre-EMI needs to be claimed over a five year period. i.e. This year you claim 1/5th of the Pre-emi amount, another 1/5th next year etc. for 5 years.
I think the person in this circumstance can get the benefit of principal amount. The EMI consists of Principal + Interest. Before possession of the house, the person can get the benefit of Principal amount in Section 80C.
But he can claim for interest part only after the possession of the house.