No, unless there are other shenanigans going on wizards only cast Arcane spells.Is this legal?
My Wizard trains the Nature skill, relating to Primal magic.
The Pathbuilder "lets" my Wizard choose Heal as a spellbook Primal spell.
(It helps the character concept − expressing good fate, sunlight, and magic.)
Your character concept sounds like it could benefit from the Magaambiyan Attendant and later Halcyon Speaker archetypes, or a version of them attuned to your setting. In Golarion, the Magaambiya is one of the pre-eminent magic schools, with a focus on both arcane and primal magic.