Regarding a 2003 2500 5.9 HD... considering these trucks come stock with dual 12v batteries and rather robust alternators, what would be considered the max amount of watts/amps one could "safely" draw from a DC/AC power inverter installed within the truck's electrical system? Interested in thoughts on both max "intermittent" & max "continuous" draw (with engine running)...

 

The max watts or amps would depend on the wire size used and of course your inline fuse or breaker. Then, you would be limited by how much time you expect to use the Inverter when the engine is off (Battery will only last so long), or if the engine is running, the watts of the alternator.

I'm not sure what you want to run, but in my '03 I ran a 140W inverter to power a string of Christmas lights in the cab while parked. The longest they ran before restarting the engine was about 4 or 5 days. Not much of a draw.

I had to wire a 12V outlet in my '15 as both outlets that came with the truck were powered only when the truck was running. The Christmas lights are on as I type.

 

probably should have been a bit more specific... previous owner installed a 1500/3000 Watt Peak DC/AC converter under one of the rear cab bench seats and though I've never plugged anything in larger than a 15.6" laptop, curiosity is getting the best of me and wondering if I could take advantage of the 1500 Watt continuous spec limit on the DC/AC converter (with the truck running) should the need ever arise(?)

 

I'm far from an electrical guru but my little brain says that roughly, 1500 watts divided by 12 volts is 125 amps.

That would be a very big load on your electrical system when you factor in the current needed to run the electrical systems of the truck, especially at an idle and depending on the temperature your grid heaters may cycle on and off putting an additional large load on your alternator, batteries and wiring.
I have run a 1,500 watt inverter temporarily for an hour or more to warm the block heater on a dead tractor in a field in the winter. It didn't seem to hurt anything but I don't think I'd want to make a habit of it.
Just my oppinion.