Hotels are familiar with the fact that guests occasionally make multiple back-to-back reservations and are accustomed to combining the stays onto one bill and placing them in one room for the whole time. Don't assume they'll notice it and combine your rooms automatically, though. Ask at the front desk or-- especially if you are planning to arrive late-- call ahead the morning of your arrival.

The main problem, as sweeper20 said, would be if you booked different room types. E.g., suite or ocean view some nights but not others. Hotels may be reluctant to give away significant upgrades just to patch your nights together. Being platinum will help, just don't expect miracles in terms of upgrades.