Buen Camino to you, enjoy and profit from this unbelievable experience!!!
Yes, a sleeping mat might be a good idea - in case an albergue is really full.
And beside, you probably might sleep better outside than inside with the stars over you, a cooling wind and the birds' songs waking you up...
I did the Camino in May - a very "busy" period as well-, and sometimes albergues got quickly 'full'...
Well, generally they help you to find an alternative with f.i. "taxi-service" (they come and take you and bring you back in the morning so that you can continue the camino exactely where you stoped the day before) but for 4 it might be a little more tricky...
Trust your Camino, and everything will be just fine.
PS for Ajda : "Alto do Poyo"...
Well, we stayed there and it was just really horrible. The worst place to be and to stay. Rather unfriendly owners, dirty, not very nice food (for a not very nice price) and when waking up in the morning, everything was wet!!! (so some of us had to put their clammy clothes on to start the day... Uuuurrrgh!!!
Not a loss if you didn't get a bed there!