Can very large count outcomes be treated as continuous variables? I have very little expertise with count outcomes and analysis of them, but I understand that, in general, they cannot be treated as continuous dependent variables for the purpose of analysis due to their "gappiness" and natural inability to take on all real values.
However, I'm wondering how one treats these variables when the counts become very large (i.e. number of cars on a highway over a year). Is it possible to treat these very large count variables as continuous and run an OLS regression, or is it still not a valid method due to the natural limitations count variables have placed on them?

Why do you want to avoid count data models? If it is lack of experience, OK, but most of what you have learnt about linear regression can still be used and useful with other models, like generalized linear models.
There are two main reasons for trying Poisson regression (or some other count regression, like negative binomial) with count data:

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*Heteroskedasticity, the variance with the Poisson distribution is equal to the mean.


*Need to take account of sampling effort, with offsets. For a detailed discussion see Goodness of fit and which model to choose linear regression or Poisson.
With large counts this aspects will not disappear!  With your highway example, some new problems might be introduced: The usual Poisson likelihood function assumes exact counts, any approximation error in the counts is not accounted for. This might destroy the proportionality of mean and variance?  Here is a paper looking into this problem.
