It would be fairly easy to run before and after database benchmarks in an app such as AnTuTu Benchmark. That would show if there are any real gains to be had.
Looking at the script, it essentially just re-writes all of the databases on the phone (via a VACUUM/REINDEX combo). Logic would state that if you have badly fragmented databases, which would manifest as things like degredation of performance over time, then this should make your phone a bit snappier.
[edit: I ran before and after tests (average of 3 tests). There was no appreciable difference between the tests. Now, the test results may not reflect real world results for two reasons: 1. I have no idea how the database I/O test in AnTuTu actually tests (what database, etc) and 2. I received errors when the script was attempting to vacuum databases ("error: unable to open file"), though the re-indexing worked fine.
End result? The test essentially means nothing and all we can go off of is anecdotal evidence. However, whether it's a placebo effect or not, this process simply can't harmfully impact your phone. As such, results should be anything from no change in response to some response increase.
Yeah, I know. A whole lot of typing that essentially says nothing. Sorry!]