I like what chl has written. Despite that, I am moved to discuss whether this situation necessarily requires a complicated model. But first, let's begin with responses to some comments.
(1) You don't lose any degrees of freedom due to spatial correlation of forest cover. This is an explanatory variable, not the one you're trying to model. You might lose "degrees of freedom" when the residuals of the dependent variable exhibit spatial autocorrelation. Such correlation is not necessarily a given even when a map of the dependent variable itself suggests strong spatial correlation. The reason is that the correlation in the map likely derives from the correlation in the forest cover (and other spatially distributed covariates). Remember, in such models you don't ask whether the "samples are independent"--it's usually obvious they are not--but whether any deviations in them from their modeled values are independent.
(2) Therefore, a conditional autoregressive model might not be necessary. I think this modeling choice would be attractive only if you want to test a theory of contagion.
Now to answer the original question: yes, first run an ordinary logistic (or Poisson) model, because as a general principle it's good to try simple (but reasonable) models first. Provided its residuals do not exhibit strong spatial correlation, you are then ok with the results. If there is evidence of correlation and evidence that it will appreciably affect your answers (coefficients, predictions, or whatever), consider using a generalized linear geostatistical model (GLM). These are described in Diggle & Riberio, Model-based Geostatistics (a relatively inexpensive and accessible text), which itself documents several R packages for making the estimates and some associated EDA tools (geoR and geoRglm). The GLM approach lets you simultaneously fit your model and assess the degree of spatial autocorrelation. The principal limitations I have found in these packages are (1) they don't handle anisotropy well--you can detect it but it's hard to incorporate it in a model--and (2) they don't have a provision for nested variograms, which somewhat limits your ability to model the spatial correlation. Both of these are no problem for smallish datasets, because you need (typically) hundreds to thousands of observations, or more, to model correlation at this level of detail.
Finally, a word about the "population" question. I assume you are interested in more than a mere description of the data: you seek information about a possible association between disease and other observable factors. Even when you have a comprehensive description of the data for a spatial region, it still does not act like a census, because the outcomes could have turned out otherwise. Next year, with identical forest cover, there will be a slightly different pattern of disease. In other regions of the country or the world and at other times, exactly the same combinations of explanatory variable values are likely to produce varying rates of disease. Thus, you're modeling a process, not a population.