yes you can run off a tank you just need to adjust the pressure at the pump
the issue is the rotary pumps dont really like to self prime
here is my set up in a rental house i am in . its simple and easy to do but its not super pretty (but works well)
if i was to put the water under the bench i would incorporate a small pressure pump to feed the rotary pump. but if your going under bench just plumb it in to the main.....
once i get back into my own house it will be plumed back into mains