Is it possible to fit skirting boards with screws into the wall
UPDATED:

I misread about the masonry walls. I've actually installed base trim using trim screws and plastic plug anchors. It works fine, but the holes in the trim are larger.



ORIGINAL: 

Glue is only used for joints, and nails pull out of the wall fairly easily when the boards are removed. They can then be pulled through the boards from the back side so the boards can be reused. 

You can certainly use screws, but the holes will be much larger and therefore more difficult to conceal. 

In general, trim isn't installed with the expectation that it'll be regularly removed.