I have MCS and in the past I've taken a screen tent and slept outside when the weather permitted.
The biggest downfall is the weight.
There are plenty of spots where you can stealth camp - just leave the place like you found it.
I've mostly found spots AFTER each village, so you can go into town, get food, then walk a ways out and find a place, sometimes in a park with tables, etc. There is no charge. Certain albergues will allow camping. Some I know of offhand are Roncesvalles, Zubiri, Hospital de Orbigo, Rabanal del Camino, and several others. Pretty much any of them with a yard are worth asking. You'll pay whatever the other pilgrims pay for the use of the shower and kitchen, usually under 8 euros.
If you do a search on tents and on camping you'll find lengthy threads about this.
Buen Camino.
I keep editing this because I keep thinking of other places.
Outside of Ciraqui is a good place if you walk the ROAD and not the Camino.
You can see a photo on my blog.
San Nicholas, San Anton have allowed camping in the past.
There are many...
I wouldn't bother taking a stove, etc.
There are many very inexpensive places to find food all along the route.