There's two ways to look at these questions: the "practical" and the "theoretical." Practical first ....
In practical terms, a new pump with new GFCI is not going to present any 'false trip' problems. If the equipment we're speaking about is less than 10 years old. chances are that the pump itself is beginning to go bad. Megger testing of the pump will reveal the fault. Powering the pump from a diferent GFCI will reveal if the first GFCI is misbehaving.
As far as the 'theory' goes, there are some simple facts to bear in mind:
First off, the UL standards for GFCI's -and, by extension, all appliances- changed about 15 years ago. The resulting GFCI's are much less prone to 'nuisance' tripping, and the appliances (pumps, refrigerators, etc.) are not supposed to 'leak' enough to cause nuisance trips.
Voiding the UL listing? Balderdash. As made plain in the UL "White Book," there's not a darn thing you can do that will 'void' a listing. The worst you can do is create a situation where UL will say, if asked, "we don't know." You want to get technical, UL won't even admit that any specific piece of hardware meets their requirements- even as it's put in a box at the factory. You're on your own. You want a 1-time specific answer, pay for a field evaluation.
Removing plugs / adding flexible cords is always fodder for endless discussions regarding their "legality." Heck, you ought to see some of the lunchroom debates at UL, as young engineers debate wire twisting and wire nuts!
If it makes anyone feel any better, there have been some recent changes to the UL standard (electrically operated pumps) that allow a far greater degree of flexibility for the installer, and this whole "modification' pilpul. UL really does not have an issue with cutting off the plug- or, for that matter- installing a cord and plug. This may come as a surprise to the dishwasher / water heater crowd, but those are different standards (and different committees). I suspect that UL can see that no one answer fits every situation, and that the responsibility rests with the AHJ.
Sure, old habits die hard. Not putting the sump pump or refrigerator on a GFCI is enshrined in many local amendments. For the worrier, there ARE GFCI devices that sound an alarm when they trip. Makes sense to me! There are also readily available alarms to tell you when the water overflows the pit.
Code is code. Design is design. The two don't mix too well.
