Would also be a good idea to completely back off the packing clamp. The packings are water lubricated and rely on water pressure to generate a small amount of leakage. About 10 drops per minute is sufficient to cool and lubricate the surface of the shaft against the packings. This isn't possible with a garden hose.
The thrust bearing is not an issue. When necessary, we run boats without a bowl and impeller.
The other issue is the impeller and wear ring surfaces abrade from dirt picked up during towing. This reduces performance by opening up the clearance.
Even if you have the garden hose plumbed into a tee fitting, water isn't fed directly to the wear ring surface. Water dumps into the bowl and the impeller gets only a little splash.
Lastly, in the event of water lubricated bowl bushings. Running dry tears up the bushings and shaft. It is not uncommon for this to be ignored until the bushings completely wear through and the bore in the bowl is damaged.
We put a lot of work into these parts and want to maximize the lifespan. We recommend, when launching, dunk the boat in the water far enough to completely submerge the pump. Pull forward so all the water flushes out any debris picked up from the road.
Impellers and wear rings are expensive. It is astonishing to see how much wear is caused by running on the trailer.