I have a template that could be used in the Snatch data tab (see the toolbox link in my signature). The number of chests of each rarity gathered per run would be sufficient (displayed when the boss dies, so you don't have to manually count, plus platinums which would need to be manually counted). Aidoru's template, which is much more detailed, could also be used (linked to in the Advent drop calcs (Ixion) tab). Each user should collect data in their own closed template to prevent vandalism.

But yes, this would be a sustained effort that would require many users over several events.

Statistically, I could do a t-test comparing drop rates across each event between the Snatch group (collected assuming 5+ stacks on the Advent boss, which is more or less guaranteed if you use Snatch on cooldown with D'art equipped with Snatch II) and no-Snatch group. Alternatively, I could pool the data and compare the overall drop rate using Fischer's Exact Test.

Caveat: Assuming a base platinum chest drop rate of 1%, Snatch would have to boost that rate to 1.3% (a 30% increase) to spot a difference using a Fischer's Exact Test with a sample size of 100. That drop rate increase may be overly optimistic (the effect on bronze chest drop rates seems to be in the 10-15% range).