Disconnect the pump, it doesn't require any break in. However, running it dry can cause damage.
First, the packings require lubrication provided by water actually leaking. On a new pump, the packings are installed fairly tight initially. Pressure in the suction housing will force water between the packings and the shaft. If you are using the graphite impregnated packings, you will start to see some black tracing where water has dripped from the packings. The black is loose graphite that has been carried with the dripping water. Monitor the dripping while under way. The drip rate should be about one drip every ten seconds. If the drip rate is excessive, tighten the packing clamp nuts evenly by about a quarter turn and continue to monitor and repeat. If the packings are leaking excessively, it can cause damage to the pump. On the hit, the impeller could pull air through the packings, pseudo cavitation which could damage the impeller and bowl. If water is spraying out, the thrust bearing could suffer water contamination. Running the pump on the hose can not supply enough water to the packings to provide sufficient cooling and lubrication.
Next, the clearance between the impeller and wear ring of a performance clearanced pump is critical to performance and efficiency. While towing, crud and road grime finds its way into the pump. Running it dry will cause abrasion of both the wear ring and impeller wear surface. Performance and life are reduced. In fact, if you are running a stainless impeller and stainless wear ring and the two come into contact while running, gauling will occur and could seize them together. A stainless impeller and wear ring require water for lubrication. Again, the garden hose just doesn't cut it.
With a race prepped pump, you will need to make changes to your boating practices. When you launch, dunk the boat quickly with the reverse bucket open, then pull the boat out to flush debris from the pump. If you feel your startup procedure warrants firing the engine out of water, it can be fired after flushing the pump, but only for a few seconds.
Do not drive the boat on/off the beach. Push it out waist-deep and bounce the stern a few times to flush sand from the pump. It's hard to believe, but one grain of sand in between the impeller and wear ring is enough to stall a big block or spin the wear ring right out of the suction housing.
Lastly, there is absolutely no reason to run the engine dry after the boat is back on the trailer. Revving the engine on the launch ramp is not going to blow the last few ounces of water out of the pump. It will take life out of your engine and pump.
There's a lot of opinions on this topic and some feel that it is perfectly acceptable to run the pump dry or on the hose. We always recommend that you don't run the pump dry. If you have to run it dry, keep it to the absolute minimum run time. Bottom line, it's your boat and your money; do what you feel is right.
Good luck,
Joe