All albergues cover their mattresses with something. In Galicia you are give a paper sheet and pillow case, in most other places there is a contour sheet and pillowcase but I doubt they are washed daily. On the Norte and Primitivo a number of albergues give you proper sheets: contour and flat, as well as a pillow case.
If you plan on sleeping in a sleeping bag or liner you may be ok with a contour sheet that has already been slept in, only you can decide. Will you also be ok sleeping directly on one without the liner or bag? Only you can decide. But know that very very few people bring a sheet and pillowcase.
I now bring a pillowcase, but you could also use your towel or a tshirt for that. I also bring large piece of tule sprayed with permetryne to cover the mattress, but very few do that. And what would it be like to sleep on directly? I went out yesterday to buy a softer yet light peice of fabric to spray and cover the matress since for the cirst time I will be sleeping with a quilt, not a bag of somesort.