Hello Joanna,
No, processing a Short year will not cause data corruption.
From your description, the program does not think that any of the depreciation for 2001 (July 2000 to June 2001), has been posted.
Processing a Short year will cause the program to create prospective adjustments on all assets that have been affected by the Short year. You will also have an opportunity to set the New Fiscal Year and First Month of the New Fiscal Year.
If you have a good backup of the data, it doesn't hurt to try it.