Caution: I am not a SAS user.
My understanding is that OLS is equal to MLE when the assumed distribution is normal.
You are falsely opposing OLS and MLE. OLS estimates are MLE parameter estimates. OLS models are appropriate for the class of models where you are modeling $\mathbb{E}(y|x) \sim \mathcal{N}( \beta_0+\beta_1x, \epsilon^2)$. But there are many alternative cases. These alternative cases are what GENMOD
was designed for.
When there are not weights specified, OLS parameters are maximum likelihood estimates.
Is there something about the use of the log link function that no longer makes OLS=MLE? I've only ever read that equivalence is simply based on the assumption of a normal distribution.
Yes. That is the manifest purpose of GENMOD
with non-identity links: to specify non-OLS models. Function GENMOD
constructs generalized linear models (GLMs). This is a class of models where the expectation of the response may be of an alternative distribution than would be assumed under an OLS model. You can still use the GLM command to build an OLS model; simply specify the identity link as you have already done!
Selecting a log link in the GLM is telling SAS that you want to build a specific kind of model: one in which $\mathbb{E}(y|x)\sim\exp(\beta_0+\beta_1x)$. For a Poisson regression model, the log link is the canonical link, and transforms your linear predictors to be on the appropriate scale of the assumed response.
There are, of course, other link functions. The most commonly used in my experience is binary regression, in which the response variable is a "yes" or "no" or a 1 or 0 or any dichotomous outcome. In this case, the link function is $\text{logit}$ and you are performing inference on the factors which cause our outcome to appear as 1 or 0.
Parameters of GLMs are estimated using MLE procedures. So the coefficients will have the desirable qualities of MLEs, provided that the usual assumptions are met.