Okay, the first caveat here is that rarefaction is a complicated discussion in general. That said, the concensus in 2019 is that rarefaction is necessary from most diversity analyses (but not all, check out breakaway plugin). It’s also not recommended for feature-based analysis anymore.
If you rarify before you do your PICRUSt prediction, you’re going to lose data from the rarefaction. But, you’re also going to come out with an uneven depth, because the prediction counts vary based on the gene prediction. So, you might rarify and still discover that your samples don’t add up to the same depth.
In terms of bias, rarefaction is still a somewhat random process, so there is the chance that your observed rarified PICRUSt table doesn’t perfectly correspond to the organisms in your observed rarefied ASV/OTU table. Beta rarefaction can somewhat alleviate this problem (with the caveat that you’re probably going to be happier running this on a smaller dataset), but you are still dealing with some noise in your model due to those differences.