Is it possible to drive 400km despite a defective water pump?

Unfortunately, the water pump is defective with my old carrot and it loses (especially in the stand) water. If I refill regularly, but everything is fine… I can’t do a repair myself and also the cheapest workshop would like to work besides 65€ for the pump 180€ – because I also need a new battery and the air conditioning system needs to be refilled, the costs slowly exceed the value by nasty dimensions… Since the car has only one year Tüv and I have it myself I don’t want to invest that anymore. But I have a friend from the fire department at 400km distance who would install me a new pump including work for 130 euros – if I somehow come down there at a bit I have already built a sensor that shows me the water level in four heights and flashes, even if the lowest contact is no longer in the water. Now I just have to get the cable in the interior… But I would prefer to use the The hose must then stop through the window But I do not have to stop and refill all 10km (not yet tested) … The question is whether I do not screw up the lid for level sensor and filling hose a) the container or b) the lid or c) the lid, but leave it open. What happens while driving with overpressure or underpressure? Do I harm the engine or anyone with an open lid?