No, Randy already had an interest in classical music long before he met Ozzy. Remember, his mother was a music teacher. Randy was a bluesier player, it's true, but then most of the soloing on both of his Ozzy albums is fairly bluesy. Only a few solos veer into neoclassical territory, even though Randy's writing chops showed a strong classical influence from the beginning.
I'm also pretty sure that Randy was an Uli Roth fan in the '70s just like Yngwie; that's really where the neoclassical thing came from.
Yngwie was a complete unknown until he sent that tape to Mike Varney in 1982. It's unlikely that he sent Ozzy a tape in 1979, considering that he was only about 16 at the time.