This is a question I am asked very regularly. The short answer is yes you can but only if you want mediocre to poor results. Here’s why:
Non-ionic surfactants are one of the most popular type of surfactants that weed killers, herbicides and other lawn chemicals call for. These products are more than just the “glue” that your controls need to make them effective they have another purpose. They all are the vehicle that allows the critical connection and transfer of the product you apply to the grass blade or leaf of the plant.
Soap is fine if you are doing a pure organic/DIY solution but for high tech weed controls you will be directly going against the product label that calls specifically for non-ionic surfactants. These surfactants are cheap, the weed controls are the more expensive part, so why cheap out on such a minor cost?
I am all for saving money but not for inferior results. NONE of the weed control companies make these surfactants, they are only specified because they are NECESSARY.
It’s up to you, but I would keep the dish soap for cleaning dishes and use what is specified for the best weed control results you can get.