You absolutely can softwash with a pump up sprayer.
You can softwash with a coffee cup also. Fill the cup up, toss it on the siding, repeat a few hundred times, dwell, rinse with garden hose, then move to the next side.
Seriously, though, If you are doing your own house, or maybe a one off for a neighbor, then yes you can use a pump up sprayer. If you want to make money at this, there are much easier methods. The easier you make it, the faster it gets done, the more money you make per hour.
Spend a week reading threads here about the basics, and you will learn a lot.