How to repair a shower corner bench
It does not appear structural, as the seat itself is still flush to the wall.  If the seat were failing the seat top would be pulling away as well.

My guess is that the panel in question was installed with a slight angle there - poor cut or something - and that the caulk used has just given up, as caulk does.  However, more camera angles showing the seat would help confirm that suspicion.

As for do you need to dry it - as long as there is only marble back there, no, water won't hurt marble.  The problem is, you can't actually tell without pulling it apart.  If there is any wood there, however, I'll be very surprised.