I have tried quite a bit over the past few years with no luck to find anything concrete and useful about this question via internet searches. My house lacks central air and is in a humid, hot environment in the summer so we use a couple window units for about 2-3 months. What I can tell you is that my experience with the window units is that they can get mildewy inside from the moisture they pull out of the air and the filters are on the INTAKE instead of output side so cool air is being blown past the mildew that gets in the blower/squirrel cage. I keep an eye on them and clean the filters and as much of the insides as I can get to & run lysol through them now and then. I have also bought new ones twice in 5 years because the mildew gets into the styrofoam and deep inside where I can't get to it. After living this way for 10 years and the last 5 with a CF tot at home, we have not found any increase in respiratory troubles during summer.
As for whether a central unit would avoid the mildew troubles, that is the question I've not been able to get answered. All ACs pull moisture out of the air and the air handler has the potential to get mildewy or worse - Legionnaire's disease comes from central air conditioners that have standing water in the air handlers; so I'm not convinced central air would put my mind completely at rest on the question.