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Constant on/off will harm the engine. Short trips followed by longer trips that do get it up to operating temps wouldn't be ideal, but would help. I don't think there's any real data out there that relates to what would happen if, and when, something bad would happen based on so many variables regarding short trips.
Your glow plugs stay on for about 2 minutes after turning the key on. Your alternator can't keep up with the draw of the glow plugs. The high compression of a diesel engine means the starter draws a lot of current, which takes some time to recharge via the alt... but you aren't even charging in the first 2 minutes. So even disregarding how mean you are being to the actual engine in doing that, you are going to be running your batteries down pretty quickly.
Would frequent short (100 feet) trips, where the engine doesn't warm up, harm the 6.0L turbo/engine?
That type of driving would harm any internal combustion engine. Besides the above noted reasons an internal combustion engine needs to be run long enough to cause the condensation in the crankcase to evaporate. Short trips cause the condensation to collect and contribute to corrosive chemical action in your engine. I would install an automatic idle controller (AIC) and let it high idle between the moves.