No, they're voracious recruiting machines. It is certainly possible to get hired by writing into a webform; it's not a particularly effective way relative to others, but it works enough to justify them sending those leads to recruiters.

Other than knowing an acquaintance that works in the company I see no other way to get into an interview more quickly. You should certainly cultivate an internal advocate. In no circumstance will that be worse than applying cold; it will often be better.