Ooo thats a good question... I would assume so, but if not, where would you go...?

Also, would it transport me to a house that was protected by a charm like the one Dumble dore used on the Dursleys when he left Harry on their doorstep.

My theory is that the Vanishing Cabinet can transport me from one house to the other if both are under Fidelius charm but with same Secret Keeper.

Was Hogwarts under the charm when the death eaters attacked in 1996?

The Hogwarts seems to have been under the charm because when Harry asked Dumbledore how can they disaparate out of Hogwarts to which Dumbledore replied that being him has its own advantages. So this implies that the charm was still working then.

This further means that Vanishing Cabinet can work even against this spell.