Depends. Generally no but I suspect if you left it turned on dry for like a Month or more you'd have issues.
The pump is what is called a diaphragm pump. there are 3 moving parts that contact water plus one more that does not plus a switch
The inlet check valve (if the tank is dry this is going to just site there)
The outlet check valve (See inlet)
The diaphragm. It has contact with only one other part (A metal plunger) and it does not move relative to said plunger so nothing for it to rub against..
The plus one is the plunger, which is inside a magnet (Solenoid style) and of course the switch (And spring) that turns the magnet on and off.
Home was where I park it. but alas the.
2005 Damon Intruder 377 Alas declared a total loss
after a semi "nicked" it. Still have the radios
Kenwood TS-2000, ICOM ID-5100, ID-51A+2, ID-880 REF030C most times