My 2 cents - The pumps shouldn't starve during start up - hull pick ups or drives, doesn't matter. Generally there is a blockage somewhere (i.e. oil cooler) that is restricting the flow. I've seen many a people have to rev the engine a couple of times to make them flow - every time I find peices of old impeller stuck in a cooler somewhere.
You lost an engine due to a pump issue?? No buzzers??