If you close off that gap, when you shut the bathroom door and turn on the vent fan, which you must do when you take a shower to keep from soaking every surface in the bathroom from the condensation, there will remain only one source of replacement air for that sucked out by the fan.
That source will be gasses sucked out of the black and gray holding tanks.
Think about that for a minute.
In fact, I've found that unless I open one of the windows in the trailer, a couple minutes of vent fan operation leaves the whole trailer stinking like sewer gas. So fill in that door gap at your peril.