You Do Need power plug adapter while traveling from Madeira to Vatican City.

Here is Why You Need An Adapter

The outlet and plug type used in Vatican City are C, F and L and in Madeira are C and F. This is how they look like.

Madeira

In Madeira, outlets of type C and F are in use.

Type C

Type F

Vatican City

In Vatican City, outlets of type C, F and L are in use.

Type C

Type F

Type L