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Completely draining a pool can cause damage and if it does, it might result in problems for you with your landlord. Best to check with the landlord before doing anything beyond keeping the status quo with relation to the pool.
Do you ever intend to use the pool? Pool upkeep may not be as expensive as you think if you take the right tack. The majority of us here at TFP keep our pools perfect using simple household chemicals (bleach, baking soda, acid) by doing the BBB method. Collectively, most of us grew weary from spending hundreds of dollars for chemicals from the pool store that you really don't need to use.
Read the Pool School articles if you would like to learn more and enjoy the pool this summer. If you find that is not what you want to do, you should discuss options with your landlord before doing anything else.