Yes it does. The ONE REQUIREMENT is that if your wife declares the rifle on her SAPS 520 (hence she is allowed to bring "her" 11 lbs of ammo), then she must be the person with the US Form 4457 for that rifle in her name. South Africa Police Services equate the US Form 4457 to a "rile permit."
Unless your wife would be prohibited from owning a rifle in your State, she must come with you when your register your rifle with US Customs (Form 4457 bearing the current year stamp) and get her own Form 4457 for her rifle.
I am assuming (?) that you use Afton House (or similar) for a pre-approved SAPS 520 and a meet & great service at the airport. If so, getting 2 SAPS 520 pre-approved is not going to add much cost to the typical $100 fee. What really costs is having one person waiting for you at international arrivals and walking you through the formalities: that cost is the same, whether only one of you, or both of you, have a SAPS 520.
My recommendation is to do everything 100% "by the book" to, at best, not turn the formalities into a stress test; or, at worst, not get your rifle/ammo impounded or God knows what else could be conjured up by a disgruntled, incompetent or power-crazed agent/officer hell bent on making your life miserable. They are rare but they exist, there just like here...