It's possible but not likely.
It's possible to have an orange object that reflects a very narrow band of wavelengths, say 589 to 591 nm, and absorbs all others. This object would be difficult to see if illuminated only with narrow-band red light (like a HeNe laser). Of course, absorbtion is also never perfect so even if illuminated with blue light it would likely be possible for a sufficiently sensitive sensor to detect the object.
But for natural objects it's much more likely that it reflects a relatively broad range of wavelengths, but reflects most strongly in the orange band. For example, an object reflecting wavelengths between 570 and 640 nm, peaking around 590 or 600 nm, would likely be perceived as orange. But 640 nm is well into the red band, so this object would be visible (and look red) if illuminated with a monochromatic red light.