Just finished the CP from Lisboa in mid-September and several places between Lisboa and Porto were already planning the "winter shutdown" due to lack of pilgrim traffic. My first three days, I saw only one or two other pilgrims, even at the albergues, until I arrived in Santarem. From that point, there were more pilgrims on the route, although it wasn't until Coimbra that I encountered more than 10-12 per day.
[Note: I am interested in going back to walk some of the sections from Santarem to Coimbra, as it was 41 degrees C for several days while I was walking in September. My experience was also different in that I took a detour to Fatima and then north to Coimbra through Pombal and Condeixa a Nova (this was bushwhacking through areas that are not normally used by CP folks), but there are albergues that primarily serve Fatima pilgrims coming from the north.]
My usual approach to finding a bed in towns that don't list accommodations, on both of my camino hikes - CF and CP - is to locate the biggest bar/cafe in town and ask where I can find a room or a bed/shower for the evening. Haven't had to sleep outside yet, as there is generally at least one place in town or nearby where there are rooms. North of Porto, there was no problem, but the first 150km out of Lisboa had some days where 25-30km between official albergue/hostels was not uncommon. As noted in a post above, the Portuguese are figuring out that the number of CP pilgrims is steadily increasing, so there are new sleeping options opening and being planned by the locals. The Portuguese, from Lisboa to Tomar, seem to focus on Fatima vs Santiago as a final destination, but that may change as more people begin walking from Lisboa to Santiago. Bom Caminho!