Putting the pink stuff in your fresh tank and pumping it everywhere should be fine for the water pump. Just make sure that (a) the antifreeze isn't too diluted by leftover water in the tank or water heater; and (b) you pump ALL the circuits (sinks, shower, toilet, outside fixtures...), to be sure all the water is purged. I guess that avoiding dilution is one of the advantages of those "winterization valve" setups, rather than dumping it in the tank.
I don't use that stuff--I winterize using compressed air. If you do that, you do have to make sure no water drains back down to the pump (I remove the clear plastic strainer cover so it drains). But, with antifreeze properly deployed, I don't see what the issue might be.
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Now: 2022 Fully-custom buildout (Ford Transit EcoBoost AWD)
Formerly: 2005 Airstream Interstate (Sprinter 2500 T1N)
2014 Great West Vans Legend SE (Sprinter 3500 NCV3 I4)
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