I walked in March last year. It was cold, wet, lots of the albergues were closed. And I didn't see another pilgrim for days on end! But I'm sure you'll enjoy yourself
In all seriousness: this is a beautiful region, and you'll get to visit some great towns and cities along the way, but as a first-timer, I hope you aren't expecting a certain type of 'camino experience'. I spent a few days walking with a first-timer in March last year, and she said that, had she known how frustrating it was going to be (with the lack of albergues, lack of pilgrims, the torrential rain), she would definitely have chosen a different path.
"... calling a couple of days ahead to see if anyone is willing to take a pilgrim in the less expensive, but usually closed, auberges?" - not sure what you mean by this? The municipal albergues are run by volunteers, who come in for very specific dates, so if they're closed, there's nobody to call. Most of the municipal albergues open for the season around Easter, maybe earlier in March if you're lucky. (You might have more luck with the private albergues - which are obviously not geared solely for pilgrims).
You will need to be prepared for the weather: it's quite mild along the coast right now, but just last week a massive storm lead to the closure of paths and beaches. When I walked last year, we were diverted a couple of times due to severe flooding. There's also a chance of snow on the Primitivo (fellow forum member Sara Dhooma did the
Primitivo last month, if you want to get an idea of winter weather on this path). Of course, you might luck out and have a few days or even weeks of beautiful sunshine... the weather can be very temperamental in this part of the world! It's just about being prepared, and managing expectations.