Here is a kernel density estimate of the "true" distribution, with bootstrapped pointwise 95% confidence bands from 999 resamples:

It looks plausibly bimodal, though one might want to construct a suitable hypothesis test for unimodality versus multimodality. Unfortunately, as you noted, we cannot distinguish between the hypothesis that the bimodality is due to rounding (at 500 M) versus the hypothesis that the bimodality is due to ambiguity between Europe and the EU. This holds even if a hypothesis test rejects a unimodal model, but if anyone is still interested in testing for unimodality, I suggest considering Efron and Tibshirani's approach using the bootstrap.

Edit: Updated the plot. I switched from adaptive bandwidth to fixed bandwidth (because it seems to achieve higher efficiency), so parts of what I wrote below are no longer relevant—I've put these parts in square brackets.

Plot notes: [The adaptive bandwidth was achieved with Mathematica's built-in "Adaptive" option for SmoothKernelDistribution, which is horribly documented; I think it uses the same algorithm as 'akj' in R's quantreg package.] A Gaussian kernel was used with the bandwidth set according to Silverman's rule-of-thumb [and the sensitivity ('alpha' in akj's documentation) set to 0.5]. The bootstrap confidence intervals are "biased and unaccelerated" because I don't (yet) understand how bias-corrected and accelerated bootstrap confidence intervals work. Tick marks on the x-axis represent the actual data with a slight jitter added to each point.