Yes, water gets pumped into the engine via a rubber impeller.
Rubber doesnt do well in dry conditions and will eventually break.

If you have been doing this all along, I do hope you have
recently changed the water pump anyhow. If you just changed
it, stop starting the engine dry NOW. If you havent changed it
in awhile, do it now while its the start of the season. Sucks
killing a perfectly good day on the water because of a bad
water pump impeller. Be careful, you can kill the engine without
it being cooled.