Not from inside the pump (assuming no damage). Keep in mind that your fuel pump is lubricated by the fuel. It is not a good idea to run it dry.
The idea is that, all restrictions between the pump and the tank should be reduced to prevent the onset of cavitation. Cavitation is essentially the forming of bubbles as the liquid gasses off in low pressure areas. Think of the saying, “You can not pull a liquid or push a chain.” In designing any pump system, an effort to reduce all restrictions to the pump inlet should be made. This includes: large diameter hose/tube, hose/tubing where the inner surface has a low coefficient of friction, fittings with smooth transitional bends, a wide mesh (low restriction) filter or no filter at all, and for ideal conditions gravity feed.
Some pumps will tolerate more Foreign Object Debris (FOD) passing through them than others. I have a hard time feeling good about FOD passing through my high dollar pump. I run a coarse mesh, low restriction filter before the pump and then a tight mesh, low micron after the pump. The fine mesh filter is to protect the fuel metering devices (carb, regulator, injection, etc.).
You will get FOD in your tank if you ever fill from the pump or siphon out of your tank. Sharp edges on the inside of the filler neck inside the tank will scrape off little bits of the siphon hose.
The best solution is to start with a clean tank and keep it that way. Filter every drop of fuel that enters the fuel system. Do not run any filter before the pump. Run a tight mesh filter after the pump.