So if I ran my bilge pump all the time I would never see this water, but
sometimes there would be no water for the bilge pump to suck out and it
would be running dry. Will this hurt the pump?


Yes.

You need an automatic switch for that bilge pump to turn it on and shut it off
depending on the water level.

Float switches can be a pain in the butt, and usually don't last very long.

I think my next pump switch willl be a:

www.waterwitchinc.com