It's probably safe. I can give you a theoretical answer. Someone who has repeatedly done it could add anecdotal evidence that theirs hasn't broken yet (or refute the idea if they tried it and it broke). Explanation:
The question focuses on the glass, so I'll start with that. Borosilicate glass has a very low coeficient of thermal expansion, making it very tolerant of high temperatures, rapid changes in temperature, and temperature differences within an item. All borosilicate glass generally has that characteristic, but the exact composition and manufacturing process varies, and not all borosilicate glass is the same. Some products could handle more extreme situations than others. But it's likely that any borosilicate glass from a reputable manufacturer could handle the temperatures and conditions encountered in food and beverage preparation.
For some context, the original Pyrex formulation was a type of borosilicate glass patented by Corning. It could be heated on the stove top or a hot plate, or go from refrigerator to oven without breaking. Some Pyrex products are still made with borosilicate glass, but the kitchenware now generally is not. It was changed to tempered soda-lime glass because that's much cheaper to make, and that is usually adequate for most household food and beverage preparation requirements.
The tempered soda-lime glass will handle oven temperatures, but not large, rapid temperature changes or differences within an item. For example, it can't be used on a stove top or have direct contact with the heating element. Laboratories that use glassware that will be heated generally stick with borosilicate glass because it is more tolerant of temperature-related issues than tempered soda-lime glass.
A disreputable manufacturer could make crappy borosilicate glass, which didn't have the thermal stability you would expect. Bodum is a reputable brand, and likely would not use substandard glass. This item was designed for a different usage. It sounds like the company has not specifically tested it on a hot plate, so they don't want to speculate.
But all that said, I suspect the issue with the stove-top use warning is not the glass, but the collar, which looks like it's made of cork and leather (and the plastic filter above that). Those could be susceptible to damage from an open flame on a gas stove, or intense heat from an over-sized electric burner. But if the bottom of the carafe is properly sized and on a drip coffee maker heating pad, that issue wouldn't be relevant. It ought to be fine.