Yes, if you can. Not having a bed that first night you arrive at your starting point sucks! It is certainly no way to start your Camino.
I always advise making a reservation. I also recommend staying two nights at SJPdP. This gives you one, extra day to prepare, shop for last minute items or souvenirs, and make arrangements before starting out.
Some folks use Express Bourricot (
https://www.expressbourricot.com/) to send a suitcase direct to Santiago, to be there waiting for you on arrival. This is an excellent way to send all your "tourist" clothing and supplies you will not need on Camino ahead of you. It is not cheap, but is absolutely reliable and secure.
If you bought souvenirs at SJPdP on that extra day off - you likely will - you can put them in the suitcase and send it down the road as well. FYI, Basque-made espadrilles are a HUGE industry there.
Hope this helps.
Tom