In a bathroom, do baseboards need to be caulked to prevent water seepage?
Caulk it.  I wouldn't leave a gap.  I'd tape the floor and apply caulk.  People clog toilets and flood bathroom floors.  I use PVC baseboards in bathroom since they are water resistant.  MDF is horrible for water but if you caulk it and have it well painted it is possible it holds up to a few water incidents.