"If I have a situation where the nearest support to the nozzle is, say, 5'- 10' away, the stress analysis program will report forces and moments acting on the nozzle for the 'gravity only' case. Depending on the piping arrangement, it is possible that these forces and moments may act in the opposite direction to those generated by the thermal expansion of the piping. This effect would make the loads on the nozzle for the 'G+T+P'case (Grav.+Temp.+Press.)lower than 'T+P', by itself."
Exactly right. You, as the competent analyst, will recognize that this is happening and account for it it your analysis.
"Now...suppose the installer 'inadvertently' connected the piping to the equipment such that were no loads on the nozzle in the 'cold' condition (i.e. 'stress-free connection'). (This could be done by adjusting or shimming supports or minor alterations to the piping). Under this sceario, the nozzle would actually see T+P and NOT G+T+P during operation .... This is why I am suggesting that it may be appropriate check if T+P is higher than than G+T+P."
As the analyst you can only account for "the normal foreseeable operating condition" unless you have a very good reason to do otherwise. This condition you report would not be a normal condition because a competent millwright/mechanic will not install the pump in this manner, thus you would not try to account for it during your analysis. THis assumes a regular design process, i.e. pre-construction. A forensic analysis is something entirely different.
This reminds me of when I took Failure Analysis in college. The prof told us the story of when he had been called in on a lawsuit where a small child had climbed up and stood on an oven door that had been lowered to the horizontal position. Well the door collapsed and injured the child so the parents sued the oven manufacturer and everybody else. The jury found that a kid standing on the door was in fact a foreseeable design condition and that the manufacturer should have anticipated that happening and should have designed the door thusly. So they lost their collective rear ends on that one.
The point is that you can only design for what you think is the usual loading conditions that the pump will see: normal operating, startup, shutdown, hydrotest, maintenance events, seismic events, support settlement, steam-out, etc. It's not possible or reasonable to anticipate eveything else. The manufacturer's published allowables are what they want you to hold to when the pump is operating to prevent things like excessive shaft deflection. Not sure I answered your question...
Thanks!
Pete