I'd say that rent payment would still be required monthly, to ensure the "two months in advance" condition was continuously satisfied throughout the tenancy. However, two months from the end of the tenancy contract there would be no more rent to pay. The landlord could not legally take back the property until the end of the tenancy if the rent for the full term had been paid, so effectively he would be forgoing the security of a deposit.
Since deposits (as distinct from payment of rent in advance) protect the landlord by acting as security against damage that may be caused by the tenant, failing to secure a deposit in addition to receiving the rent in advance would represent an increased risk to the landlord, but would be no disadvantage to the tenant.
I cannot see any legal problem in this, or any disadvantage to the tenant, except having to find the money to pay two months rent in advance.