I bounced around in a Cub and some other light or STOL aircraft at a few Florida airports a few years back when they had 3 or 5 hurricanes roll through that state.
My guess is that hurricanes aren't modeled as a complete system in MSFS; rather, what you get are a number of individual, local surface observations, (er, METARS). So you can experience the effects at various locales over time, but if you gassed up a hurricane hunter and cruised out to the eye, you wouldn't 'see' anything since FS WX is just weather-reporting site data downloaded periodically.
Just a theory... If anyone has tried the latter, I welcome your input.