I asked the same thing last year. I have a 250 gal. cistern with a 1" outlet, no electricity, and a need to wash equipment. My pressure washer list a minimum gal/min. and I did not feel I had that. At first I ran a small Honda water pump to pump water to my pressure washer but that was a real pain. I got a 1" suction hose (you can make one from Home Depot stiff tubing and readily available fittings (Northern has them). I hook the 1" end to the tank and the 3/4 end to the pressure washer. This seems to work fine. If you have not bought a washer, some even say in the owners manual that they will "draw" from a tank, but mine doesn't and it seems to work fine. So far, no damage. Elevating your tank would help.
My little Honda pump from Northern works great also for watering, and hosing things off (more pressure than my home hose) but it's not a pressure washer. I use it a lot to water trees in the neighborhood during recent drought. My municipality also uses the Honda pump for the same purpose, so they hold up to commercial use. The are really light weight and small. I keep it in my truck bed box. But if you need to knock off mud from equipment, the pressure washer, of course, is much better.
I agree that I would not use a garden hose to supply the washer, but a hose that will not collapse made for this purpose. I think you would be safe to try it.