The mechanisms that cool the freezer work not by cooling the food directly, but by holding the temperature inside the freezer at a constant 0°F (-18°C). A freezer at any temperature above 0°F will not perform as expected, and will not keep food at the expected temperature.
A manufacturer's instruction booklet is intended specifically to ensure the product operates as expected. While undoubtedly safety and legal concerns are a factor in their instructions, the primary concern is simply instructing the user how to operate the device under expected operating conditions.
As such, a freezer includes instructions to bring it down to 0°F prior to placing any food in it, as that ensures the freezer operates under correct conditions.
The manufacturer does not include instructions for suboptimal operation, unless said suboptimal operation is an expected condition (such as instructing a driver how to operate their car in very hot or very cold weather). A user who wishes to operate the device under suboptimal conditions does so at their own discrection. This is in part due to legal/safety concerns, but the primary reason is that the manufacturer does not want to support said usage; if they included instructions in their manual for operating their device in a suboptimal fashion, they likely would field calls from users either wanting to know how to operate it, or frustrated buyers who have spoiled food because they operated it per the manual's instructions (even with warnings that it is suboptimal).
A freezer that is not at 0°F likely will still keep food "safe" to some extent, as the food "danger zone" is only above 40°F; likely less than 30 degrees below the beginning temperature of the room. Between that and the original temperature of the frozen food, it's unlikely that the frozen food would pass above 40°F unless it was very low in mass, and certainly not for several hours (as the freezer likely is below that temperature within an hour).
Food placed in the freezer immediately after the freezer was plugged in would very likely partially thaw, unless it had very high mass (for example, if you entirely filled the freezer with frozen goods), or a relatively high freezing point. Even then, some of the food would partially thaw on the outside (though this happens anyway in a automatic defrost freezer).
If the question is, however, "if I have frozen food, and nowhere else to store it, is it better to put it in the freezer than leave it outside," I would say that the freezer is undoubtedly your best choice. The food may or may not stay frozen - again, odds are it won't - but if it's food that can stand to thaw and refreeze without too much quality damage, it's probably going to be okay, and if there's no actual freezer option, that may be your best shot. It's not going to hurt the freezer, just the food. Just be aware that the food will probably thaw, might warm even into the danger zone for a bit, and take that into consideration. I would place a thermometer in the freezer to see the temperature of the freezer, and using a laser thermometer to temp the outside of the food, to ensure that it stays cold enough; and depending on how warm it gets, adjust the expiration date of the food down.