Yes, you are correct and you seem to understand the tax law. You cannot just add them into the cost basis when you sell. Improvements are a depreciable asset just like the original house. For this reason you should consider completing the Form 3115 to take advantage of the depreciation you haven't claimed in the past. Even if you should have a passive loss carryover, you can use all of that in the year of sale. There is only benefit to you by taking advantage of this opportunity the IRS allows.
The improvements would be dated when they were placed in service so it would be a different date than when the house was placed in service.
@Anonymous
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