If you think there is "sludge" in the tank, then it needs to come out. It isn't that hard, remove the rear valance, disconnect the fuel line and fuel gauge wire, support the tank and remove the 2 9/16 strap nuts.
To your question, you should be able to remove the sending unit without dropping the tank. You might want to put an electric pump on the fuel outlet and see if it pulls fuel before removing the sending unit, it might be something else like a blocked line, bad pump, plugged filter, etc.