Well, I wish you all the best on your test.
Also, in this 'dynamic' universe, saying something has been proven is like looking back at Victorian times and saying cars will never replace horses (as horses drop dung maybe?
).
Anyway, back to positive: if serendipity does have a small effect (just as the tier of your main weap may now do), even a 1 % difference would be very interseting news. Unfortunately, you already have 4500 skill points, and I'd expect the main part of any gain curve to be noticable earlier.
Also, a big question is how to nail the randomness. In my view, you will need to record every loot and see the line that results from normal loots. It would be a bit like slowly maxing a weap and watching as the average hit slowly rises as the stats improve... not possible to tell from a few hits, but noticable statistically over time.
It can then be hoped that the serendipity gains, if they exist, are not pooled and repaid in the globals, or so. The effect would be there, but would require even more stats to show this up! I've not put in that sort of work, I admit.... but if I were to study it, then that is what I would advise.
So, I wish you 'serendipity!'.