Not really. However, you can get the information associated with each test - i.e. the analyses, options, local variables, outputs by creating a new test in a new adexl view, and then using the "Load State" form in the ADE XL test editor (or via RMB over the test name), picking directory, and navigating to the "test_states" dir within the old adexl view. You'll be able to load a state called something like theOldTestName_active.
You won't get any global variables you've altered, or any specs, or any corners, or any parameterization, but at least you should be able to recover the test set up this way.
I don't know why the data.sdb would have gone - I've not seen that happen before.
Perhaps using some design management software might be a good protection against this happening in the future?