Yep, You can set it up to suck direct from your existing tank. You will need a filter inline somewhere, but its exactly the same principle as sucking water from your wheelie bin. Although, if you just use tap water for the pressure washer, you will need to rinse your tank out preety well before using pure again.
I dont know how pure water would affect the pump...porbably wouldnt do it any hard, but then again, i dunno. Yeah mate, a filter somewhere between your tank, and the water inle into your pressure washer. so, the hose that your water is being sucked into the machine, get a filter in that hose somewhere..