They will no longer let you sleep on the floors, and by 'they' I mean every albergue.
There will not necessarily be a bed for you. You might have to walk strange hours, or longer/shorter distances than you anticipated to find a bed at an albergue. Or, you might have you pay to stay in a casa rural or hotel if space is all gone.
When I walked the Camino 3 years ago, these things happened a few times. And when all the beds were gone, they were always very strict about no sleeping on floors (it is due to fire regulations, and if they get caught they can be shut down). The only time where there was no where to sleep in more than 20 km in any direction and I thought I would have to sleep under a bridge, the hospitalera took me home with her to sleep in her house. As long as you are flexible, you'll probably find a place to sleep. But with it being holy year, I don't know!
So, yeah. Like others said, if you are camping, that is the only possible way you would need a mat. Otherwise you'll dump it. If you decide you need one while you are on the walk, you can always find one in a 'free' box, or you can buy one in a city you pass through.