Yes, but ... why would you do it? If you think your backpack is too heavy from the start, then maybe it’s better to leave some of the extra pounds at home. This will be an advantage later - along the whole length of the Camino!
Whatever you can leave at home ... all the better. That sounds like a cliché, but once on your way you will realize how true it is. You'll be surprised to realize how little you really need.
Of course there are no "hard" standards, but you can use this rule of thumb: your backpack "should not" weigh more than 10-15% of your body weight. Especially if you do not plan to camp.
If you decide to have your backpack transported: Express Bourricot runs daily from Saint-Jean to Roncesvalles. "Express Bourricot" is run by Caroline, who also speaks English. You can call her (tel. (0033) (0) 6 61 96 04 76) or mail.