Answer:  

Dr. Dean E. Riechers, who is actually studying surfactant effects on weeds, kindly answered the question above:
 
 

Nonionic surfactants are very common for agricultural applications of herbicides. The function of a surfactant (an abbreviation for "surface active reagent") is to spread the spray droplet evenly over the leaf surface, help it to adhere to the leaf, and increase penetration of the herbicide within the spray droplet into the waxy cuticle that covers the leaf surface.

Weed killer From EPA, with permission

 
Just applying water to a waxy leaf surface would cause the spray droplet to bead up, so surfactants greatly facilitate spray coverage and aid in enhancing herbicide uptake (and of course the weed dies much better as well!).
 
You are right in that surfactants do include detergents. Detergents act as an interface between water and something that is not very water soluble (like the dirt and grease on clothes, or for plants the waxy cuticle layer on the leaf surface). I am not sure if adding some common household detergents (like dishwashing liquid) would work as well as agricultural grade surfactants, but if the goal is to save some money and just do some simple spraying around the yard then it is probably worth a try. It may also be helpful to slightly increase the rate of herbicide if the homeowner wants to try the household detergent as a surfactant.
 
I hope this helps, good luck with killing those weeds!
  
 
Acknowledgement:
We would like to thank Dr. Dean E. Riechers for his kind answer.
 
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