Yes, you can add the second as a rental before it is rented.
Any renovations that are considered as improvements will be added to the cost basis of the property and will be depreciated. This TurboTax help article lists some improvements that will be added to the basis along with repairs that can't be deducted as an expense until the property is rented.
From Coleen3:
You can deduct expenses once the property is placed in service.
Placed in Service
You place the property in service in a rental activity when it is ready and available for a specific use in that activity. Even if you aren’t using the property, it is in service when it is ready and available for its specific use.
Example
On April 6, you purchased a house to use as a residential rental property. You made extensive repairs to the house and had it ready for rent on July 5. You began to advertise the house for rent in July and actually rented it beginning September 1. The house is considered placed in service in July when it was ready and available for rent. You can begin to depreciate the house in July.
@lorrainejeanes
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