Is "vanilla" random forest regression appropriate when dependent variable is a rate (i.e. per 100 people)? To add a little more context, I am working with a dataset from which I want to predict the population-normalized count of emergency department visits on county level, with 50+ independent variables. The dataset itself contains raw counts of the ED visits, as well as the county populations, so I have a bit of freedom in terms of how I perform the normalization.
I am really struggling to determine an appropriate methodology to analyze this now, however. I know with more traditional generalized linear models, careful attention needs to be given to the distribution of the dependent variable. I assume the best way to do this in a general circumstance would be a Poisson regression with an offset, though I do not know how this translates to tree-based ML methodologies, which I am specifically interested in.
With this in mind, would a "vanilla" random forest regressor (or gradient boosting, alternatively) be appropriate to use here without giving these details too much thought? I have done some digging online for an answer to this, with mixed results. I've seen that sklearn has different criterion parameters - such as Poisson - when implementing an RF, but I don't know if that is really what I need. Would regular squared error still work?
Also, as a side note, part of my analysis intends to assess a random forest/gradient boosting methodology, specifically, for this application - which is why I would prefer not to use a different type of model if I can get away with it.

You could start with a count data regression model, if only as a baseline. Then, in place of calculating rates, you model the counts and use (log of) county population as an offset.
These ideas can be used also with trees and forests. See the page how-to-handle-the-exposure-offset-with-boosted-trees. There is an R implementation in CRAN package partykit, see function glmtree.  There is more information at https://stackoverflow.com/questions/57037995/r-partykit-how-do-i-use-the-offset
